Think of this dessert as a French cheesecake: flaky, buttery pate brisee is filled with a rich combination of farmer cheese and creme fraiche, which becomes puffed and golden after a turn in the oven.
Pulse flour, sugar, and salt in a food processor until combined. Add butter; pulse until mixture resembles coarse meal. With machine running, add 1/4 cup ice water in a slow, steady stream, just until dough holds together. To test, squeeze a small amount together; if it is crumbly, add up to 1/4 cup more ice water, a little at a time. Do not process more than 30 seconds. Divide dough in half; flatten into disks. Wrap each in plastic; refrigerate at least 1 hour and up to 2 days, or freeze up to 3 months; thaw overnight in refrigerator before using.
On a lightly floured surface, roll out one disk of dough to a 12-inch round. Fit dough into a 9 1/2-by-2-inch round fluted tart pan with a removable bottom, pressing dough up to rim of pan. Freeze until firm, about 1 hour.
Preheat oven to 375 degrees with rack in center. Place pan on a rimmed baking sheet. Line dough with parchment, pressing it into corners and edges; fill with dried beans or rice. Bake until edges are golden, about 30 minutes. Remove parchment and beans or rice. Continue baking until crust is light golden brown, about 10 minutes more. Transfer sheet to a wire rack and let cool completely.
Reduce oven temperature to 350 degrees. In a medium bowl, whisk together 1 cup sugar and flour. In another medium bowl, whisk together farmer cheese, creme fraiche, egg yolk, salt, and vanilla; using a wooden spoon, stir in butter, followed by sugar mixture.
In the bowl of a mixer fitted with the whisk attachment, beat egg whites on medium speed until foamy. Increase speed to medium-high and gradually add remaining 1/3 cup sugar. Continue beating until medium glossy peaks form, about 4 minutes. Fold half the egg whites into cheese mixture to lighten, then fold in remaining egg whites.
Transfer filling to tart shell. Bake until filling is just set (it should barely wobble when very lightly shaken), 45 to 55 minutes. Transfer sheet to a wire rack; let cool 1 hour. Tart is best served slightly warm but can also be served at room temperature.