Make the Biscuit Dough: In a large bowl, whisk together the flour, baking powder, and salt. Cut in the cold cubed butter using a pastry cutter or food processor until coarse crumbs form. Stir in 1 cup of milk to create a shaggy, slightly sticky dough. If needed, add a bit more milk or flour to get the right texture. Shape into 8–9 thick discs with floured hands. Chill in the fridge until ready to use.

Make the Filling: In a large skillet, melt the butter over medium heat. Add onions, carrots, celery, mushrooms, and garlic. Cook for about 5 minutes, stirring often, until vegetables have softened. Stir in the flour, salt, pepper, and thyme. Gradually stir in the broth and milk and cook until thickened into a creamy consistency, about 7–9 minutes. Remove from heat and stir in mixed vegetables and parsley. Let cool slightly.

Assemble the Casserole: Preheat oven to 400°F (204°C). Transfer filling into a greased 2.5–3 quart baking dish or 9-inch deep-dish pie plate. Arrange cold biscuit dough rounds on top. Brush biscuit tops with remaining 2 tablespoons of milk.

Bake: Bake for 25 minutes, then increase oven temperature to 425°F (218°C) and bake for another 5–6 minutes, or until biscuits are golden brown.

Serve: Let cool for 5 minutes before serving. Enjoy warm!