1. Heat olive oil in a large skillet over medium heat. Add onion and carrot; saute 5 minutes. Add Italian seasoning and red pepper flakes; cook 5 minutes. Add tomatoes and garlic; reduce heat to low and cook, stirring occasionally, 10 minutes.
2. Meanwhile, peel shrimp and remove tails; set aside. Prepare pasta according to package directions, adding broccoli florets to the pot for the last 2 minutes of cooking. Drain and set aside.
3. Add shrimp to the tomato sauce; cook 2 to 3 minutes, until opaque.
4. Serve shrimp and sauce over pasta and broccoli.