Preheat the oven to 350°F (175°C).
In a large skillet, melt the butter over medium heat. Add the diced onion and cook until softened, about 4 minutes.
Add the minced garlic and sliced mushrooms to the skillet and cook for another 3-4 minutes until the mushrooms are tender.
Sprinkle the flour over the vegetables in the skillet and stir to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually whisk in the chicken broth and milk, stirring constantly until the sauce thickens, about 5 minutes.
Add the dried thyme, salt, and black pepper to the sauce and stir well.
In a large mixing bowl, combine the cooked turkey, thawed mixed vegetables, and mushroom sauce. Mix until evenly combined.
Transfer the turkey mixture to a 9×13-inch baking dish and spread evenly.
Sprinkle the prepared cornbread stuffing evenly over the top of the casserole.
Sprinkle the shredded cheddar cheese over the stuffing layer.
Bake uncovered in the preheated oven for 35-40 minutes, or until the casserole is bubbly and the cheese is melted and golden brown.
Remove from the oven and let the casserole rest for 5 minutes before serving.