Cook the bacon in a large Dutch oven over medium heat until crisp, about 5 minutes. Remove the bacon. If there's excess bacon grease, drain off all but 2 tablespoons. Add the onion, bell pepper, Italian seasoning, chili flakes, salt, and pepper. Cook for 5 minutes, until fragrant.
Add the broth, canned tomatoes, and chicken. Simmer over medium heat for 20 minutes, until the chicken is cooked through. Shred the chicken.
Stir in the spinach, sun-dried tomatoes, and gnocchi. Add 1 cup of water. Cook for 2 minutes. Stir in the milk and both cheeses.
Ladle the soup into bowls. Top with bacon and rosemary. Enjoy, preferably with a crusty piece of bread.
