In a small bowl, mix together egg yolks, vinegar, and 8 tablespoons of ice water.
In a large bowl, combine the all-purpose and rye flours and salt. Add the butter, and toss to coat. Using your hands, pinch the pieces of butter between your thumbs and pointer fingers to flatten them into thin shards of butter, toss to fully coat in flour. Continue until all the butter has been flattened, working quickly to prevent butter from getting too warm.
Pour the egg mixture over the flour mixture, toss with your hands to incorporate the ingredients.
Drizzle over the remaining 1 to 2 tablespoons of ice water as needed, a little at a time, just until the dough comes together and is no longer dry and crumbly. You may not need all of the remaining 2 tablespoons, depending on the humidity of the day, or you may need a bit more. You want to add just enough water for the dough to feel firmly held together and smooth rather than dry and crumbly, but not so much that it’s soft, wet, and sticky to the touch.
Pat dough out into a disc about 1-inch (2.5 cm) thick. Using a bench scraper or knife, slice disc into quarters and stack pieces on top of one another. Gently pat out the dough with your hands into a disc about 1-inch (2.5 cm) thick. Repeat the cutting and stacking once more. This process is going to give you all those flaky layers.
Divide dough into 2 discs, wrap tightly in plastic wrap and chill for at least 2 hours or, ideally, overnight. Allow dough to sit at room temperature for a few minutes to soften slightly before rolling it out. You only need one disc for this recipe, so the remaining disc can be frozen for future pie or galette cravings.