brown the veggies: Melt the butter in a 4-quart dutch oven (use oven-safe if you don't want to transfer to a casserole dish) over high heat. Add the mushrooms and allow them to brown, about 5 minutes. Add the celery and let it cook for about 3 minutes or until slightly softened. Sprinkle the flour over the veggies and stir to coat evenly. You'll notice it starts getting dry and crumbly, let cook 1 minute. Season with the dried thyme, all-purpose seasoning, and garlic powder (if using).
make the base: slowly stream in the milk while you use a whisk with the other hand to work out any lumps. Add the chicken broth and allow the soup to reach a simmer, this will take 8-12 minutes. While the soup reaches a simmer, position a rack in the center of the oven and preheat the oven to 425ºF. Once the soup reaches a simmer, add the shredded chicken, onions, crinkle cut carrots, and peas. Stir and allow the mixture to come back to a simmer.
bake: Spray a 9x13 baking dish with nonstick spray. Transfer the prepared chicken mixture to the dish. Top with the shredded cheese and the tater tots. You'll need more if you're using a baking dish and less if you're using a dutch oven. Bake for 27-32 minutes or until the tots get nice and golden brown. I like to turn the broiler on for the last 1-2 minutes just to give them a little more of a crisper texture. Let cool slightly before serving.