Instructions

for the dough

Process flours, sugar, and salt in food processor until combined, 2 to 3 pulses. Add butter and pulse until butter is cut into pea- to hazelnut-sized pieces, about 10 pulses. Transfer mixture to medium bowl.
Sprinkle water and vinegar over mixture. With rubber spatula, use folding motion to mix until loose, shaggy mass forms with some dry flour remaining (do not overwork). Transfer mixture to center of large sheet of plastic wrap, press gently into rough 4-inch square and wrap tightly. Refrigerate for at least 45 minutes.
Transfer dough to lightly floured work surface. Roll into 11- by 8- inch rectangle with short side of rectangle parallel to work surface. Using bench scraper, bring bottom third of dough up, then fold upper third over it, folding like business letter into 8- by 4-inch rectangle. Turn dough 90 degrees counterclockwise. Roll out dough again, perpendicular to edge of work surface, into 11- by 8-inch rectangle and fold into thirds. Turn dough 90 degrees counterclockwise and repeat rolling and folding into thirds again. After last fold, fold dough in half to create 4-inch square. Press top of dough gently to seal. Wrap in plastic wrap and refrigerate for at least 45 minutes or up to two days.

for the filling

Cover potatoes and microwave until just tender, 4 to 8 minutes. Meanwhile, heat 1 tablespoon olive oil in 12-inch skillet over medium heat until shimmering. Add shallots and rosemary, cover, and cook, stirring occasionally, until shallots are tender and beginning to brown, 5 to 7 minutes. Transfer shallot mixture to bowl with potatoes. Stir in olives, crème fraîche, and lemon zest. Season to taste with salt and pepper and set aside.

to bake

Adjust oven rack to lower middle position, place pizza stone on oven rack, and heat oven to 400 degrees. Remove dough from refrigerator and let stand at room temperature for 15 to 20 minutes. Roll out on generously floured (up to ¼ cup) work surface to 14-inch circle about 1/8-inch thick. (Trim edges as needed to form rough circle). Transfer dough to parchment-lined rimmed baking sheet. With plastic drinking straw or tip of paring knife, cut five ¼-inch circles in dough (one at center, and four evenly-spaced midway from center to edge of dough). Brush top of dough with 1 teaspoon olive oil.
Spread half of filling mixture evenly over dough, leaving two-inch border around edge. Sprinkle with half of goat cheese, cover with remaining filling mixture, and top with remaining goat cheese. Drizzle remaining teaspoon olive oil over filling. Carefully grasp one edge of dough and fold up outer 2 inches over filling. Repeat around circumference of tart, overlapping dough every 2 to 3 inches; gently pinch pleated dough to secure, but do not press dough into filling. Brush dough with egg and sprinkle evenly with kosher salt.
Lower oven temperature to 375 degrees. Bake until crust is deep golden brown and filling is beginning to brown, 35 to 45 minutes. Cool tart on baking sheet on wire rack for 10 minutes. Using offset or wide metal spatula, loosen tart from parchment and carefully slide tart off parchment onto cutting board. Sprinkle with parsley, cut into wedges, and serve.