1. Cook pasta according to package directions; drain.
2. As pasta water comes to a boil, heat oil in a large heavy saucepan over medium heat. Add onion and cook, stirring occasionally, until translucent and softened, 6 to 7 minutes. Add garlic and cook 1 minute more, stirring occasionally. Add tomatoes, peppers, oregano, rosemary, salt and pepper; bring to a boil, reduce heat and simmer until sauce is reduced slightly, about 15 minutes.
3. Remove sauce from heat, remove rosemary sprig (if using) and stir in basil. Transfer to a food processor and puree, leaving a few chunks if desired. Top pasta with sauce and Parmigiano-Reggiano and garnish with basil.