Use a bench scraper to cut butter into ½-inch cubes. (If butter begins to "sweat," dust with flour.) In a large, flat-bottomed bowl, combine flour, sugar, and salt. Add the butter cubes and toss to coat with the flour mixture. Use a pastry blender to cut the butter into the flour; do not smash or smear the butter. Scrape butter off the pastry blender during the mixing process and continue mixing. (If butter is softening too fast, put the bowl in the refrigerator until butter firms up, 2–5 minutes.) Continue cutting, working quickly, until butter is broken down and looks like a coarse crumble with only a few larger pieces.
Combine vinegar with water and ice; you’ll use 10–12 tablespoons of this liquid in the pie dough. Begin by sprinkling 4 tablespoons of liquid over the flour mixture; use a bench scraper or your hands to incorporate until the mixture begins to come together. Sprinkle in 4 more tablespoons of liquid and continue the mixing process. Squeeze a fistful of dough: if it holds, like wet sand, it’s ready. If it falls apart, add 1–2 more tablespoons of liquid at a time, squeezing the dough to check if it holds. Bring all the dough together, sprinkling dry bits with more small drops of liquid as necessary; dough will look shaggy. Knead in the bowl just until incorporated.
Turn dough onto a work surface and use a bench scraper to divide dough into two equal pieces. Shape into flat disks and wrap in plastic. Refrigerate for at least 30 minutes, preferably overnight. (Note: Dough can be refrigerated for up to 3 days and frozen up to 1 month, tightly wrapped.)
Crust: Remove one dough disk from the refrigerator. (Save the other one for another pie.) Generously grease a tart pan with butter. Roll the dough into a circle 2–3 inches larger than a 10” pie or tart pan, all the way around. Remove the ring of the tart pan, leaving the only bottom. Lay dough onto the bottom by gently folding the dough in half, then aligning the crease with the center of the pan. Unfold the dough, straighten, then fold the edges of dough towards the center so the bottom will fit inside the ring.Place the tart ring around your forearm; place the bottom on your hand, then bring the ring up to meet it. Unfold the edges of the dough, then fold in any excess dough that hangs over the rim so that the top of the crust is flush with the rim. Use your thumbs to press and flatten the dough into the fluted inner edge of the ring to secure the crust as it bakes. Place in the freezer for at least 20 minutes, or until firm. Meanwhile, preheat oven to 375 degrees F.
Parbake crust: Remove the pan from the freezer and use a fork to prick holes throughout the dough. (This is called "docking," which helps maintain the shape as the crust bakes.) Cover snugly with aluminum foil. Fill the shell with ceramic pie weights; push them toward the edges, which keeps the crust from shrinking as it bakes. Place on a rimmed baking sheet and bake for 20 minutes, or until the crimped edges are set but not browned. Remove from the oven and lift the foil and pie weights out of the shell. Let the shell cool. Lower the oven heat to 350 degrees F.
Filling: In a mixing bowl, combine farmer cheese and milk. Stir well to remove large lumps. Add honey and salt, and stir well. Whisk eggs in a separate bowl, add to cheese mixture, and whisk until well blended; then stir in thyme.
Assembly: Pour the filling into the shell and bake on the middle rack of the oven for 35–40 minutes.
Pie is finished when the edges are set and puffed slightly and the center is no longer liquid, but still somewhat wobbly. (The filling will continue to cook and set out of the oven.) Cool completely. To serve, remove outer tart ring and place on another platter; serve at room temperature or chilled.