Heat ½ tablespoon of olive oil in a 10-inch skillet over medium-high heat.
While the oil is heating, season the chicken pieces with ⅛ teaspoon of salt and the black pepper.
Brown chicken 1–2 minutes per side, then transfer to a plate. (It will finish cooking in the oven.)
Add ½ tablespoon of olive oil to the pan, reduce heat to medium, and cook onions until translucent, about 2 minutes, stirring often. Add garlic and cook 30 seconds more.
Raise heat to medium-high, add mushrooms, and cook about 2 minutes, stirring occasionally.
Stir in chicken broth and bring everything together.
Remove skillet from heat. Stir in sour cream, heavy cream, cheddar, mozzarella, remaining salt, and Italian seasoning.
Add browned chicken and cooked spaghetti; toss until coated.
Transfer to a greased 5x5-inch baking dish. Place dish on a rimmed baking sheet.
Cover with foil and bake 25 minutes.
Remove foil, sprinkle with Parmesan and parsley if desired, and serve hot.
Notes
Note: If using cooked chicken, skip the first steps for cooking the chicken and begin at Step 5.
Prepare Ahead: Read the recipe and ingredient notes first. Have everything measured and ready since this dish comes together quickly.
Easily Doubles: To make Chicken Tetrazzini for two, double the ingredients and bake in two 5x5-inch dishes, one 8x1½-inch round pan, or one 9x5-inch loaf pan.
Turkey Option: Swap chicken for turkey, perfect for using up holiday leftovers.