Instructions

for the craquelin

  Process flour, sugar, and salt in food processor until evenly combined, about 5 seconds. Add butter and process until mixture resembles crumbly cookie dough, about 30 seconds. Transfer mixture to counter (do not wash food processor) and knead until uniform dough forms. Transfer to large sheet of parchment paper and press to ½-inch thickness. Cover with second piece of parchment and roll dough into 11 by 15-inch rectangle (it's fine to trim and patch dough to achieve correct dimensions). Remove top piece of parchment and use 1½-inch round cutter to cut 60 circles (A). Leaving circles and trim in place, replace top parchment and transfer to cookie sheet. Freeze until firm, at least 30 minutes or up to 2 days.

for the pastry cream and choux aux craquelin

Whisk 2 cups milk and ¾ cup sugar together in small saucepan. Cut vanilla bean in half lengthwise. Using tip of paring knife, scrape out seeds. Add vanilla bean and seeds to milk mixture. Bring to simmer over medium heat. Remove from heat and cover to keep warm. Use fork to whisk eggs together in 2-cup liquid measuring cup. Fit pastry bag with ½-inch round tip.
Bring remaining 1 cup milk, remaining 2 tablespoons sugar, butter, water, and salt to boil in medium saucepan over medium heat, stirring occasionally. Off heat, stir in flour until incorporated. Return saucepan to medium heat and cook, stirring constantly and using smearing motion, until mixture registers between 175 and 180 degrees, about 5 minutes.
Transfer hot mixture to food processor (do not wash saucepan) and process for 10 seconds to cool slightly. With processor running, add beaten eggs in steady stream and process until incorporated, about 30 seconds (do not wash liquid measuring cup). Scrape down sides of bowl and continue to process until smooth, thick, sticky paste forms, about 30 seconds. (B).
Weigh out 1¼ pounds of paste for choux buns. Transfer to prepared pastry bag, twist top closed, and set aside. Discard vanilla bean (or reserve for other use) and transfer warm milk mixture to now-empty 2-cup liquid measuring cup. With processor running, add milk mixture in steady stream to remaining choux paste and process until incorporated, about 30 seconds. Scrape down sides of bowl and continue to process until mixture is smooth, about 30 seconds longer.
Transfer pastry cream to now-empty saucepan, scraping processor bowl well. Cook over medium heat, whisking constantly and being sure to scrape corners of saucepan, until mixture has consistency of thick pudding, 4 to 5 minutes. Remove saucepan from heat; scrape corners of saucepan with spatula and whisk again until smooth. Transfer to large wide bowl and whisk to remove any remaining lumps. Press lightly greased parchment paper directly on surface and refrigerate until set, at least 2 hours or up to 24 hours.
Adjust oven racks to upper-middle and lower-middle positions and heat oven to 375 degrees convection. Lightly spray 2 rimmed baking sheets with vegetable oil spray and dust lightly and evenly with flour. Rap edge of sheets firmly on counter to dislodge and discard excess flour. Using 1½-inch round cutter, mark 30 circles on each baking sheet. Pipe choux paste into mounds on prepared sheets, using circles as guide and stopping just short of the edge of each circle (C). Place 1 frozen craquelin disk on top of each mound (D). Bake until golden brown and firm, about 20 minutes.
Remove sheets from oven and use paring knife to poke ¼-inch hole into bottom of each bun to release steam. Return choux aux craquelin to oven, turn off oven, and prop open oven door with handle of wooden spoon. Let dry until centers are mostly dry and surfaces are crisp, about 20 minutes. Transfer sheets to wire racks and let cool completely.

for the croquembouche

Fit clean pastry bag with ¼-inch round tip. In large bowl, whisk cream to stiff peaks. Gently whisk pastry cream until smooth. Fold pastry cream into whipped cream until combined. Transfer one-third of mixture to pastry bag. To fill choux aux craquelin, insert pastry tip ½ inch into opening and squeeze gently until cream just starts to appear around opening, about 1 tablespoon cream per bun (E). Refill bag as needed.
Set up assembly station near stove (F): Tape 9-inch parchment round to cardboard cake round and tape cardboard round to turntable or platter; fill medium saucepan with water and bring to boil (for cleaning caramel-coated utensils); place long-handled kitchen spoon, 2 forks, and pair of tongs (to safely retrieve anything that falls into hot caramel) on plate. Fill bowl with ice water (for unlikely event of caramel burn).
Combine sugar, water, and corn syrup in heavy-bottomed saucepan and cook over medium heat, without stirring, until sugar has dissolved, 6 to 10 minutes. Continue to cook until mixture is amber-colored, 8 to 10 minutes (if mixture is coloring unevenly, gently swirl saucepan). Slide saucepan off heat and allow caramel to cool to consistency of warm honey, about 4 minutes. Adjust heat to lowest setting and return saucepan to burner to keep warm.
Arrange 10 buns in circle, so they are touching one another, on cake round. Remove 3 buns from circle (G). With long-handled spoon, drizzle about 2 teaspoons caramel onto cake round where buns were (H). Working quickly, return spoon to saucepan and place buns on drizzled caramel (I). Repeat with remaining buns until all 10 buns are attached to round.
Drizzle about 1 tablespoon caramel over about one-quarter of bun circle. Arrange 3 buns on hot caramel, positioning them about ¼ inch toward middle of circle, pressing gently and holding buns in place until caramel cools slightly, about 15 seconds (J). Repeat until second layer has circle of 9 buns. Continue to build 6 more layers, using one fewer bun for each successive layer and always placing buns about ¼ inch toward middle of circle to achieve cone shape.
For second-to-last row, place 1 bun flat side up on counter and drizzle with caramel. Carefully place second bun flat side down on hot caramel. Let cool slightly, about 1 minute. Drizzle top of croquembouche with caramel and stand double bun vertically on top. Drizzle top of double bun with caramel and stand last bun vertically on top. Slide caramel off heat and let cool slightly.
Holding 2 forks back-to-back, dip into caramel to coat both sets of tines. Drizzle caramel around croquembouche, turning turntable, if using, to cover with thin caramel strands (K). Repeat until croquembouche is coated to your desired appearance. If desired, drizzle about 1 tablespoon caramel onto parchment paper to make decorative topper (star, spiral, etc.). Let cool until solid, about 5 minutes. Make slit in top bun and insert topper, if using, shortly before presenting. Serve within 2 hours. To serve, use tongs to pluck individual buns from structure; if necessary, use kitchen shears to cut caramel between buns. (Leftovers may be refrigerated for up to 2 days, but buns will soften and caramel will become sticky.)