Preheat your oven to 375 degrees Fahrenheit (190°C).
Making the pot pie filling
In a large saucepan, melt the butter over medium heat. Add the onion, carrots, and celery, and cook until the vegetables are tender, stirring occasionally. Stir in mushrooms and cook for another minute.
Sprinkle the flour over the cooked vegetables and stir for a 1-2 minutes to cook off the raw flour taste.
Gradually whisk in the chicken broth and milk, then add the dried thyme, salt, and pepper. Allow the mixture to simmer and thicken for a few minutes. Taste and adjust seasoning to your liking.
Stir in the cooked turkey (or chicken). Remove the saucepan from the heat.
Assembling the pot pie
Transfer the turkey (or chicken) mixture to a 9x13 inch baking dish and set aside.
Prepare the cheddar bay biscuit mix according to the package instructions or your homemade recipe.
Drop spoonfuls of the biscuit dough over the turkey or chicken mixture in the baking dish. The biscuits should touch and overlap to ensure all the filling has some biscuit topping to go with it.
Place the baking dish in the preheated oven and bake for 25-30 minutes, or until the cheddar bay biscuits are golden brown and the filling is bubbling.
Finishing with garlic butter
While it bakes, melt the remaining butter and whisk it together with garlic powder and fresh parsley.
Remove the dish from the oven and brush the biscuits with garlic butter.