Heat olive oil in a large pot over medium heat. Add garlic and onion and cook for 3–4 minutes until soft and fragrant.
Increase heat to medium-high. Add zucchini and bell pepper; cook for 1½ minutes.
Add crushed tomatoes, broth, tomato paste, herbs, garlic powder, chili flakes, salt, and pepper. Stir well.
When the liquid begins to bubble, reduce heat to medium. Add pasta and stir.
Top with broccoli, pushing it slightly into the liquid.
Cover and cook for 5 minutes.
Remove lid and cook another 3–4 minutes, stirring frequently, until pasta is almost tender and liquid is mostly absorbed.
Stir in half the cheese if using. Adjust seasoning.
Sprinkle remaining cheese on top, cover, and let sit 1 minute until melted.
Garnish with parsley and serve immediately.