1 2/3 cups all-purpose flour, plus more for surface
3 tablespoons sugar
1 tablespoon active dry yeast (from two 1/4-ounce envelopes)
1/2 cup warm water
1 large egg yolk
1/4 teaspoon salt
7 tablespoons unsalted butter, softened, plus more for bowl and pan
1 cup sugar, divided
1 tablespoon all-purpose flour
1 3/4 cups (14 ounces) farmer cheese, room temperature
1/2 cup (4 ounces) creme fraiche, room temperature
1 large egg yolk, plus 3 large egg whites, room temperature, divided
1/4 teaspoon salt
1 teaspoon pure vanilla extract
1 tablespoon unsalted butter, melted
1/2 cup applesauce
1. Dough: Mix together flour, sugar, yeast, water, egg yolk, and salt in the bowl of a stand mixer fitted with the dough hook until a dough is formed, about 3 minutes. Add butter, and mix until incorporated, about 3 minutes (dough will be sticky). Transfer dough to a buttered bowl, cover with plastic wrap, and let rise at room temperature until almost doubled, about 1 hour. Punch down dough, cover, and let rise 30 minutes. Refrigerate dough, still in bowl and covered, until firm, about 2 hours.
2. Punch down dough. Roll out into a 12-inch round on a lightly floured surface. Fit dough into a buttered 9 1/2-by-2 1/2-inch fluted tart pan with a removable bottom, pressing dough up to rim of pan. Prick dough all over with a fork, cover loosely with plastic wrap, and let rise 30 minutes.
3. Filling: Preheat oven to 350 degrees with rack in lowest position. Whisk together 3/4 cup sugar and the flour. Whisk together farmer cheese, creme fraiche, egg yolk, salt, and vanilla; stir in sugar mixture, then butter, with a wooden spoon.
4. Beat egg whites with a mixer on medium speed until foamy. Raise speed to medium-high, and gradually sprinkle in remaining 1/4 cup sugar. Beat until medium glossy peaks form, about 4 minutes. Fold half the egg whites into cheese mixture to lighten, then fold in remaining egg whites.
5. Spread applesauce in crust, and pour filling on top of applesauce. Bake 30 minutes, then check crust; if it is starting to brown significantly, tent edge with foil. Bake until crust is deep golden brown and filling is puffed, golden, and just set (it should barely wobble when very lightly shaken), about 25 minutes. Let cool, undisturbed, on a wire rack 1 hour. Unmold tart, and let cool at least 30 minutes. Tart is best served slightly warm but can also be served at room temperature.