Combine the base. Place chicken breasts at the bottom of the slow cooker. Pour crushed tomatoes and chicken broth over the top. Add diced onion, garlic, Italian seasoning, red pepper flakes, salt, and black pepper. Stir gently.
Slow cook. Cover and cook on low for 6 to 7 hours, or on high for 3 to 4 hours, until the chicken is very tender.
Shred the chicken. About 30 minutes before serving, use two forks to shred the chicken directly in the pot.
Add dairy and pasta. Stir in the heavy cream, grated parmesan, and dry pasta. Cover and cook on high for 25 to 30 minutes until the pasta is tender, stirring occasionally.
Finish and serve. Stir in half of the mozzarella cheese until melted. Serve in bowls topped with remaining mozzarella, fresh basil, and croutons.