Preheat oven to 425ºF.

Heat oil in a large high-sided sauté pan or Dutch oven over medium-high heat. Once hot, add mushrooms and onion; cook 7 to 8 minutes, until soft.

Stir in garlic, thyme, poultry seasoning, salt, and pepper; cook 1 more minute, until aromatic.

Sprinkle flour over vegetable mixture and stir to combine. Cook for 2 full minutes, stirring occasionally, to eliminate raw flour taste.

Pour in milk and vegetable broth, and whisk continuously until smooth. Increase heat and bring mixture to a simmer; continue to let bubble until thickened, about 3 to 5 minutes.

Add frozen vegetables, white beans, and Parmesan (or nutritional yeast); stir until everything is well-combined. Turn off heat.

Grease an 8x8-inch baking pan or 9-inch deep-dish pie plate with cooking spray. Transfer vegetable pot pie filling to the pan, and spread to create an even layer.

Roll the pie dough into a circle large enough to cover your dish. Carefully place the dough over the baking dish so that it hangs over the sides. Trim the overhang to ½ inch larger than edge of the dish.

Gently press the dough onto the sides of the dish so that it sticks, and use the prongs of a fork to crimp the edges.

Brush dough with the egg wash, and use a sharp knife to cut 4 slits in the top.

Transfer pan to the oven, and bake for 25 minutes, until the top is golden and filling is bubbly.

Let stand 5 to 10 minutes before serving. Garnish with extra thyme leaves, if desired.