Preheat and prep: Heat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with cooking spray or butter.
Brown the turkey: Warm a large skillet over medium heat.
Add olive oil if needed, then the ground turkey. Break it up with a spatula and cook until no longer pink, about 5–7 minutes. Season with half the salt and pepper, plus the smoked paprika and oregano.
Sauté the veggies: Add onion and bell pepper to the skillet.
Cook 3–4 minutes until softened. Stir in mushrooms and cook another 2–3 minutes. Add garlic and spinach; cook just until the spinach wilts.
Taste and season with a pinch more salt and pepper if needed.
Layer in the dish: Spread the turkey and veggie mixture evenly in the prepared baking dish. Sprinkle half the shredded cheese over the top.
Whisk the eggs: In a large bowl, whisk eggs, milk, remaining salt and pepper until well combined and slightly frothy. Stir in Parmesan if using.
Combine and top: Pour the egg mixture over the turkey and veggies.
Gently shake the dish to distribute the eggs. Top with the remaining shredded cheese.
Bake: Place the dish on the center rack and bake 28–35 minutes, or until the eggs are set in the center and the edges are lightly golden. A knife inserted in the middle should come out clean.
Rest and serve: Let the casserole rest 5–10 minutes before slicing.
Garnish with green onions or parsley, and add hot sauce if you like a kick.