Preparation

Make and Roll the Dough

• Combine the flour, sugar, and salt in a stand mixer fitted with a paddle attachment (or if mixing by hand, in a medium bowl). Cut the butter into 1/2-inch cubes and add them to the flour. On low speed, mix the butter and flour until the flour is no longer white and holds together when you clump it with your fingers, 1 to 2 minutes. If there are still lumps of butter larger than the size of peas, break them up with your fingers. Run a spatula along the bottom of the bowl to loosen anything stuck to the bowl. (If mixing by hand, mix with a pastry cutter or two forks until the butter is mixed into the flour as above).

  In a small bowl, mix the egg yolk and milk and add them to the flour mixture. On low speed, mix until the dough just comes together, about 15 seconds; the dough will be somewhat soft. (If mixing by hand, add the yolk mixture to the flour and mix gently with a fork until the liquid is well distributed. The dough will still look crumbly and dry. Dump the dough onto a clean counter and work it with the heel of your hand, pushing and smearing it away from you and gathering it up with a bench scraper and repeating until the dough comes together and is pliable).

  Turn the dough out onto a sheet of plastic wrap, press it into a flat disk, wrap it in the plastic, and let it rest in the refrigerator for 15 to 20 minutes (or up to four days) before rolling it out.

  Position a rack in the center of the oven and heat the oven to 350*F. Line a heavy-duty rimmed baking sheet with parchment. Remove the dough from the refrigerator; if the dough is very firm, let it sit at room temperature until it’s pliable enough to roll, 10 to 15 minutes. On a floured surface, roll the dough into a round that’s about 13 to 14 inches in diameter. It’s all right if the edges are a little ragged. If you can’t get a roughly round shape, trim the dough so that it’s a rough circle and roll the trimmed scraps back into the dough. Transfer the dough round to the baking sheet and put it in the refrigerator while you prepare the filling.

Assemble and Bake the Tart

• Put the apples in a large bowl. Toss the fruit with the 1/4 cup granulated sugar. Taste the fruit; if it’s more tart than you like, add up to 2 Tbs. more sugar. Add the flour, vanilla extract, cinnamon, and salt and toss until everything is evenly mixed.

  Remove the dough from the refrigerator and let it sit at room temperature for about 5 minutes to keep it from cracking when you assemble the tart. Heap the apple mixture in the center of the dough round. Using your fingertips, fold the edges of the dough over some of the apples to create a rim about 2 inches wide. Work your way all around, pleating the dough as you go.

  Using a pastry brush, brush the pleated dough evenly with the beaten egg. Sprinkle the turbinado sugar directly on the dough and fruit.

  Bake the tart until the pleats of dough are completely golden brown without a trace of pale, unbaked dough, about 55 minutes. (It’s all right if some of the juices escape from the tart and seep onto the pan.) Transfer to a rack and let cool. The tart may be baked up to six hours ahead of serving.

  When cool enough to handle, use a spatula to transfer the tart to a serving plate or cutting board. Slice it and serve it warm or at room temperature.