Preheat the oven to 400 degrees F. Lightly coat an 8x10 or similar 2 1/2-quart casserole dish with nonstick spray. Set aside.
Heat a large dutch oven or similar deep, heavy-bottomed pot over medium-high heat. Add 1 tablespoon of the oil to the pan. Once hot but not smoking, add the mushrooms and cook for 8 minutes, until the mushrooms are beginning to brown, stirring occasionally. Add the garlic powder, salt, and pepper. Cook until the mushrooms have browned more deeply, about 3 additional minutes.
Sprinkle the flour over the top of the mushrooms. Drizzle in the remaining 1/2 tablespoon oil. Stir and cook until any white bits of flour disappear and the flour looks light golden, about 1 to 2 minutes. The mixture will seem dry. Slowly pour in the milk. Switch to a whisk and stir constantly. Bring to a low, gentle boil, continuing to whisk and scraping any brown bits from the bottom of the pan. Continue to let bubble until thickened and reduced by about half, about 7 minutes, whisking very often. Turn off the heat. Stir in the chicken, frozen vegetables, and thyme. Taste and add additional salt and pepper as desired. Spoon the chicken mixture into the prepared dish.
Drop the biscuit dough by rounded spoonfuls over the top, dispersing the biscuits evenly over the surface. Some of the filling will peek through.
Bake until the biscuits are golden brown on top and cooked through, 25 to 30 minutes. Let cool 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). The biscuit batter can be refrigerated and stored separately up to 1 day ahead.
TO STORE: This recipe tastes best the day it is made, 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.
TO FREEZE: Freeze leftovers in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.
TO MAKE VEGETARIAN: Substitute an additional 2 cups of chopped vegetables for the chicken.