Instructions

for the doughnuts

Stir flour, sugar, and yeast together in bowl of stand mixer. Add milk and egg and mix with rubber spatula until all ingredients are moistened. Fit stand mixer with dough hook and mix on medium-low speed until cohesive mass forms, about 2 minutes, scraping down bowl if necessary. Cover bowl with plastic wrap and let stand for 20 minutes.
Add salt and mix on medium-low speed until dough is smooth and elastic and clears sides of bowl, 5 to 7 minutes. With mixer running, add butter, a few pieces at a time, and continue to mix until butter is fully incorporated and dough is smooth and elastic and clears sides of bowl, 7 to 13 minutes longer, scraping down bowl halfway through mixing. Transfer dough to lightly greased large bowl, flip dough, and form into ball. Cover bowl with plastic. Let sit at room temperature for 1 hour. Transfer to refrigerator and chill overnight (or up to 48 hours).
Adjust oven racks to lowest and middle positions. Place loaf pan on lower rack. Line rimmed baking sheet with parchment and grease parchment. Transfer dough to lightly floured counter. Press into 8-inch square of even thickness, expelling as much air as possible. Roll dough into 10 by 13-inch rectangle, about ½ inch thick. Using 3-inch round cutter dipped in flour, cut 12 rounds. Transfer doughnuts to prepared sheet. Bring kettle or small saucepan of water to boil.
Pour 1 cup boiling water into loaf pan. Place sheet on upper rack, uncovered. Close oven and allow doughnuts to rise until dough increases in height by 50 percent and springs back very slowly when pressed with your knuckle, about 1 hour.
About 20 minutes before end of rising time, add oil to large Dutch oven until it measures about 1½ inches deep and heat over medium-low heat to 330 degrees. Set wire rack in second rimmed baking sheet and line with triple layer of paper towels. Using both your hands, gently place 4 risen doughnuts in oil. Cook until golden brown on undersides, 1½ to 2 minutes, adjusting burner as necessary to maintain oil temperature between 325 and 340 degrees. Using spider skimmer, flip doughnuts and cook until second sides are browned, 1½ to 2 minutes. Transfer doughnuts to prepared rack. Return oil to 330 degrees and repeat with remaining doughnuts. Let cool completely, about 20 minutes.

for the filling and coating

Place sugar in small bowl. Spoon jam into pastry bag or zipper-lock bag fitted with ¼-inch round pastry tip.
Working with 1 doughnut at a time, coat all sides of doughnut in sugar and return to rack. Insert paring knife through side of 1 doughnut until tip almost reaches opposite edge. Swing knife through doughnut, creating large pocket. Repeat with remaining doughnuts. Stand doughnuts slit side up in 13 by 9-inch baking pan.
To fill doughnuts, insert pastry tip ¾ inch into opening and squeeze gently until jam just starts to appear around opening, about 2 tablespoons jam per doughnut. Let doughnuts stand in pan for 10 minutes to allow jam to settle. Serve.