Heat olive oil in a large pot over medium-high heat. Add onion and garlic and cook until tender, 5 to 7 minutes. Add diced tomatoes, chicken broth, basil, oregano, cayenne, salt, and pepper. Reduce heat to low and let simmer for 20 minutes.
Transfer mixture carefully to a blender in batches and puree; return to the pot. Stir in Gorgonzola cheese, orzo, and sour cream. Continue to simmer until heated through, 5 to 10 minutes.