Heat oven to 375°F; lightly grease 9x13-inch dish.
Melt butter in large skillet over medium; cook onion about 5 minutes until softened, then garlic another minute until fragrant.
Sprinkle in flour; stir to coat and cook 1-2 minutes to remove raw taste.
Gradually whisk in broth and milk to prevent lumps; simmer 3-4 minutes until thickened.
Add turkey, frozen vegetables, thyme, salt, and pepper; warm through about 3 minutes. Remove from heat.
Spread turkey mixture evenly in dish.
Spread potatoes over, making peaks and swirls with spoon or spatula for crisp edges. Add optional cheese.
Bake 25-30 minutes until top golden and edges bubbling. Rest 5 minutes before serving.