1) To start dough, mix together flours with sugar and salt. Cut in cold, cubed butter using your fingers or pulse in a food processor until the butter is in pea-sized pieces.
2) Stir in water and vinegar and mix until the dough is saggy. It’s okay if it doesn’t come together completely at this point. Don’t overmix it.
3) Scoop dough out onto plastic wrap. Form dough into a rough rectangle (again, it will still be crumbly). Wrap very tightly in plastic wrap and refrigerate for at least an hour.
4) Remove dough and roll into a long rectangle, about 8×14 on a well-floured surface. Fold the left 1/3 of the dough into the center, then fold the right 1/3 over it. Rotate the dough 90 degrees, roll it out again, and repeat the fold. Do this one more time. If your dough sticks to the counter, use a dough scraper to scrape it up and use more flour. Then fold the dough (which should be much easier to work with now) into a square and wrap it in plastic wrap again. Refrigerate for another hour.
5) For filling, wash mushrooms and add to a microwave safe bowl. Cover with plastic wrap and microwave on high for 4-5 minutes until soft. Drain mushrooms in a colander. When cool, slice thinly.
6) Slice leeks thinly using just the white and light green sections. Add sliced leeks to a large skillet with a drizzle of olive oil. Cook over medium heat until the leeks are soft, about 4 minutes. Add fresh thyme and sliced mushrooms and continue to cook for another minute or two until the mixture is fairly dry.
7) Remove filling from heat and let cool. Then season with a pinch of salt and pepper and stir in sour cream and mustard.
8) When ready to make galette, preheat oven to 400 degrees. Remove dough from fridge 10-15 minutes before making the galette. Roll the dough out into a large 14 inch diameter circle. Use a knife to cut off any edges. Try to make it as round as you can, but it’s okay to eyeball it.
9) Transfer the dough to a baking sheet lined with parchment paper. Brush the center of the dough with olive oil.
10) Add half of the filling to the center of the dough, leaving about 2 inches around the edge. Add 1/2 of the gorgonzola cheese. Top with the rest of the filling and then the rest of the cheese. Drizzle with olive oil.
11) Fold one end of the circle in toward the center, then work around the galette, making folds every few inches.
12) Brush galette with egg wash and transfer to oven. When galette is in oven, turn heat down to 375 and bake for 35-40 minutes until the crust is golden brown.
13) Let cool briefly and serve immediately!