Cook chicken in olive oil with spices. Remove and cook the peppers and onions in the same pot.
Melt the butter and add the garlic, then deglaze with broth and add cream cheese, heavy cream, shredded cheeses, tomatoes, and seasonings.
Cook until cheese melts, then add cooked pasta, chicken, and vegetables to the pot. Reduce heat to low and simmer for 15-20 minutes.