1egglightly beaten with 1 tablespoon water to create an egg wash
Place rack in the lower third of the oven. Preheat the oven to 425 degrees F. Lightly coat a 9-inch pie dish with baking spray. Set aside.
Heat a large Dutch oven or similar deep, heavy-bottomed pan over medium-high heat. Add the butter. Once hot, add the mushrooms and cook for 6 minutes, until mushrooms are beginning to brown, stirring occasionally. Add the celery, garlic powder, salt, and pepper. Cook until the mushrooms have browned more deeply and the celery begins to soften, about 3 additional minutes.
Sprinkle the flour over the top of the vegetables and cook 2 minutes, until the white disappears (the vegetables will seem dry). Slowly pour in the almond milk, adding a few splashes at a time, stirring constantly. Bring to a low boil, scraping any brown bits from the bottom of the pan. Continue to let bubble until thickened, about 3 to 5 minutes, stirring very often and scraping a spatula along the bottom of the pot to prevent sticking. Stir in the beans, peas and carrots, onions, thyme, and vinegar. Spoon the mixture into the prepared pie dish.
Roll the pie dough into a circle large enough to cover your dish. Brush the edges of the pie dish with the egg wash, then lay the dough over the top so that it overhangs the sides. Trim the overhang to a 1/2 inch larger than edge of the dish. Gently press the dough onto the sides of the dish so that it sticks, then brush all over with the remaining egg wash. With a sharp knife, cut 5 slits in the top.
Line a rimmed baking sheet with parchment and place the pie dish on top. Bake until the pie is hot and bubbly on the inside and the crust is deeply golden, about 20 to 25 minutes, rotating the pan 180 degrees F halfway through. Let rest a few minutes. Serve hot.
TO MAKE AHEAD: The filling can be prepared ahead of time and stored in the refrigerator for 3 days or frozen for up to 3 months (let thaw overnight in the refrigerator before reheating). Add the crust just before baking.
TO STORE: This recipe tastes best the day it is made because the crust is the most crisp, but you can store leftovers in the refrigerator for up to 4 days.
TO REHEAT: Reheat gently in the microwave or oven at 350 degrees F until hot.
TO MAKE GLUTEN FREE: Use your favorite gluten free pie crust.
TO MAKE VEGAN: Use olive oil in place of the butter and a dairy-free pie crust.