Preheat oven to 350 degrees. Set a large pot of salted water to boil. Once boiling, add spaghetti and cook just before al dente. Drain and set aside until late.
Add olive oil to a large oven-safe braising dish and set over medium heat. Season chicken with salt and pepper. Add to hot pan and cook completely. Remove from pan and set aside. Add chopped onions and cook until softened. Add garlic and cook until fragrant, about 30 seconds.
Add chicken broth and stir to break up the browned bits on the bottom of the pan. Add in cream cheese and cream of chicken soup. Let sit until cream cheese softens. Stir all ingredients together until smooth. Add mozzarella cheese and stir until melted.
Cut chicken into small pieces. Add to sauce. Add in cooked spaghetti and toss until completely coated in the sauce. Note: if your braising dish is not large enough to hold all the spaghetti, transfer sauce and cooked spaghetti to a casserole dish and combine there.
Bake casserole in preheated oven for 20 minutes or until edges start to crisp. remove and serve immediately.