Boil spaghetti in salted water until al dente (per package instructions). Drain and set aside.
In a large skillet, heat olive oil and butter over medium heat. Add diced onion and sauté until translucent (3-4 minutes). Add garlic and cook for 30 seconds until fragrant.
Stir in cream of chicken soup, cream of mushroom soup, chicken broth, sour cream, salt, pepper, and paprika. Whisk until smooth and simmer for 5 minutes.
Add shredded chicken and cooked spaghetti to the sauce. Toss until evenly coated.
Fold in 1 ½ cups of cheddar cheese and ½ cup mozzarella until melted.
Transfer to a greased 9x13-inch baking dish. Top with remaining cheese and bake at 350°F (175°C) for 15-20 minutes until bubbly and golden.
Sprinkle with fresh parsley and serve hot.
