Add the flour, sugar and salt to a food processor and pulse just until combined. In a small bowl, whisk mix together the egg, vinegar and water. Add the cold butter pieces and cheese into the food processor and pulse until small coarse crumbs remain. Sprinkle the water/egg mixture over the flour and pulse again until the dough comes together.

Remove the dough with your hands and wrap it in plastic wrap. This dough makes enough for 2 galette crusts, so you can either separate it into 2 sections now, or separate it after it’s refrigerated. Refrigerate the dough for 30 minutes.

After 30 minutes, preheat the oven to 400 degrees F.

Heat a large skillet over medium-low heat. Add the butter and olive oil. Stir in the mushrooms and garlic. Cook until the mushrooms soften, about 8 minutes. Stir in the salt, pepper, thyme, parmesan and mascarpone cheese.

Remove the crust from the fridge. Roll one of the pie crusts into a… “rustic” shape – no shape necessary really – until it is about 1/4 inch thick. Place the dough on a parchment-lined baking sheet. Sprinkle half of the cheese on the crust. Layer the mushrooms in the center leaving a 2-inch+ border of crust. Sprinkle on more cheese. Once the mushrooms are layered, fold the crust over top of the mushrooms. Brush the crust with the beaten egg wash.

Bake the galette until the crust is golden, about 40 to 45 minutes. Remove, let cool slightly and sprinkle with herbs. Serve immediately.