Heat olive oil in a large Dutch oven or pot over medium heat. Add the diced onion and cook until softened, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the tomato paste, Italian seasoning, dried basil, and optional red pepper flakes. Cook for 1-2 minutes, stirring constantly, to toast the paste and seasonings.

Pour in the crushed tomatoes and chicken broth. Stir everything together, scraping up any browned bits from the bottom of the pot. Season with salt and pepper. Add the chicken breasts to the pot, ensuring they are submerged in the liquid. Bring to a simmer, then reduce heat to low, cover, and cook for 20-25 minutes, or until the chicken is cooked through.

Carefully remove the chicken breasts from the pot and place them in a bowl. Use two forks to shred the chicken. Return the shredded chicken to the soup.

Turn the heat to low. Slowly stir in the heavy cream and grated Parmesan cheese. Continue to stir gently until the cheese is melted and the soup is creamy. Do not let the soup boil after this point.

Ladle the hot soup into bowls. Top each serving with a generous sprinkle of shredded mozzarella cheese and fresh basil. Serve immediately.