Preheat the oven to 350 degrees F (175 degrees C). Place 2 tablespoons butter in a 9x13-inch casserole dish.
Place casserole dish in the preheating oven to melt butter. Remove from oven, leaving heat on, and spread the melted butter around the dish to coat the bottom.
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in egg noodles and return to a boil. Cook noodles uncovered, stirring occasionally, until tender yet firm to the bite, about 6 minutes. Drain.
Melt remaining 2 tablespoons butter in a large skillet over medium heat. Add mushrooms and onion; cook and stir until onions are soft, about 5 minutes. Add ground turkey. Cook, breaking the meat up, until browned and crumbled, 5 to 7 minutes more. Season with salt and pepper. Add mushroom soup, sour cream, and meatball seasoning packets. Stir well, adding milk, until sauce is thickened to desired consistency, 3 to 5 minutes more.
Combine the egg noodles and sauce; place in the casserole dish. Cover with aluminum foil.
Bake in the preheated oven until top is bubbling, about 30 minutes.