Place the flour and salt in the bowl of a food processor and pulse to combine. Remove the lid and top with the cold butter chunks. Replace the lid and pulse 30-35 times, or until the mixture resembles a coarse meal with the butter in pea-sized chunks.
Mix the vinegar with the milk in a measuring cup. With the processor running, add the milk through the feed tube until the mixture begins to clump and form a ball. Remove from the processor on a lightly floured work surface and flatten into a disk. At this point, the dough can be wrapped in plastic wrap and chilled, or assemble the galette with the cooled roasted squash and leeks.
Prepare the squash:
Preheat the oven to 400 degrees. Toss the squash slices with the olive oil, honey, cayenne, and enough salt to season well. Place in a single layer on (2) rimmed baking sheets, being sure not to overcrowd the pan or the squash will steam instead of roast. Bake for 30-35 minutes until nicely softened but not mushy. Cool.
Prepare the leeks:
Heat the butter and oil in a large sauté pan over low heat. Add the leeks and salt, and sauté until coated with the butter and oil. Place a parchment lid over the leeks, which is a square of parchment paper with a small hole cut out in the center. This will steam the leeks gently to soften.
After 20 minutes, remove the lid, and increase the temperature to medium low, careful not to burn the leeks. When the leeks are caramelized, about 15 - 20 more minutes, remove from heat and cool.
Assemble the galette:
Roll the dough out in a large circle ⅛" thick, and roll it loosely around a rolling pin, then unroll it onto a large cookie sheet.
Mix the cooled leeks with the 2 tablespoons of Greek yogurt, and add salt and pepper to taste. Spread over the dough, leaving a 1½" border around the edges to fold the dough over.
Layer the squash over the leeks in a decorative patter, overlapping slightly. Top with the grated cheese. Fold the dough over, crimping and overlapping the edges, then brush with the egg wash.
Bake at 400 degrees until the galette begins to brown, about 15 minutes, then reduce heat to 375 degrees and bake until golden brown on the top and the bottom, about 15-20 minute. Cool 5 minutes on wire rack, and serve warm. Enjoy!
Notes
Total time above includes cooking the leeks and the squash at the same time, and cooling the squash and leeks before assembling.
The dough, squash, and leeks can all be made ahead, and stored in the refrigerator until ready to use. Just roll out the dough, assemble, and bake!