Cook pasta according to package directions, omitting salt and fat; drain.
Heat olive oil in a large skillet over medium heat. Stir in onion, carrot, and garlic; sauté 3 minutes. Stir in 2 tablespoons Parmesan cheese and next 4 ingredients (through cannellini beans); simmer 5 minutes. Stir in spinach, and cook 1 minute or until spinach is wilted. Stir in pasta; cook until thoroughly heated. Divide pasta mixture evenly. Sprinkle evenly with remaining 2 tablespoons cheese and breadcrumbs.