Mushroom Galette with Thyme, Garlic, and Chevre

Servings 8 people

Whisk the egg with vinegar and 3 tablespoons of ice water and set aside. Follow instructions below, depending on if you want to make the crust by hand, or if you want to use a food processor.
MANUAL METHOD: Mix together the flour, sugar, thyme, salt, garlic powder, and cream of tartar in a large wide bowl. Using a box grater, grate the butter using the large hole setting of the grater above the bowl, stopping to stir with a fork and coat the butter bits in the flour mixture every 10 seconds or so. When all the butter is in, pinch the mixture together with your fingertips until it resembles the texture of damp sand. Add the water, a tablespoon at a time, mixing it with a fork, until the dough just holds together when you squeeze a fistful of it in your hand.
FOOD PROCESSOR METHOD: Cut the butter into individual tablespoons and set aside. Place the flour, sugar, salt, sage, onion powder, and cream of tartar in the food processor and pulse a few times to mix together. Add the slices of butter and pulse until the butter is reduced to roughly pea-sized pieces. Run the machine while you add the egg mixture, letting it blend for 5 seconds after the liquid is added. Do NOT overmix. Add the remaining ice water, 1 tablespoon at a time, pulsing as you add it, until the dough just holds together. It shouldn't be too wet and sticky, nor should it be super crumbly.
Divide the dough into two equal portions, wrap in beeswrap or plastic wrap, and place them in the refrigerator for 1 hour.

Heat 2 tablespoons of the oil in a large saucepan over medium high heat. Add the onions and reduce heat to medium low and stir to combine. Cook until the onions are transparent and lightly golden around the edges, about 12 minutes, stirring every few minutes.
Add the garlic and cook for 5 minutes more until the garlic is very fragrant, stirring every minute or so. Add 1 teaspoon of the sherry vinegar, then the add mushrooms, salt, thyme, sage, pepper, and the remaining tablespoon olive oil. Stir to combine. Cook until the mushrooms release their water, have softened and darkened in color and are fragrant, and the water they released has evaporated, about 20 to 25 minutes more, stirring every 5 minutes or so. Stir in the last teaspoon of the sherry vinegar, remove from heat, and allow the mixture to cool to room temperature. After it's cooled, stir in the crumbled chevre. If preparing the filling the day beforehand, place the filling in an airtight container and refrigerate overnight.

Preheat the oven to 375 degrees Fahrenheit. Roll out one portion of the dough into a circle and trim off 2 inches around the edge. Cut decorative shapes (leaves, etc) from the 2-inch border piece and set them aside. Lightly brush the decorative cut-outs with the egg wash, then lightly brush the circle with the egg wash, and place the decorative cut-outs on it. Use a small knife to poke 3 vent holes in different parts of the crust. Place the decorated circle in the freezer for 30 minutes to help solidify it.
Roll out the other portion of the dough into a large circle about 1/8-inch thick. Transfer it to a lipped baking sheet lined with parchment paper (it's okay if the edges hang over a bit, we'll be folding it back over the filling). Evenly distribute the cooled mushroom filling in the center of the circle, leaving a 2-inch border of emptiness around the edges. Place the decorated circle on top of the mushroom filling, and fold the edges of the lower crust up over the upper crust. Lightly brush the exposed edges of the folded crust with the egg wash. Place the pan in the oven and bake until the crust is deeply golden, about 50 minutes.