Melt butter in a large skillet or Dutch oven over medium heat. Add onion, mushrooms, salt and pepper. Cook until onions are soft and fragrant, about 4 minutes.
Transfer mixture to a slow cooker and add the chicken broth and mushroom soup. Stir mixture until combined. Add the chicken breasts in a single layer and submerge in the liquid.
Cook on high heat for 4 hours or low heat for 8 hours. Remove chicken from the slow cooker and shred using two forks. Add shredded chicken back to the slow cooker.
Add the cream cheese and mozzarella, stir, and cook on high heat for an additional 30 minutes, or until the cheeses have melted.
Ten minutes before cook time is up, cook the spaghetti noodles on the stove top according to package directions.
Serve chicken and cream sauce over the cooked noodles. Top with fresh parsley and serve!