Heat 1 tbsp olive oil in a large pot over medium heat. Add 2 minced garlic cloves and 1 finely chopped onion. Cook slowly for 3 to 4 minutes until the onion is translucent and sweet.
Turn heat up to medium-high. Add 2 sliced zucchinis and 1 sliced red capsicum. Cook for 1 1/2 minutes.
Add 800g crushed tomatoes, 1.5 cups broth, corn, and broccoli florets. Stir until the tomato paste dissolves. (Do not add pasta yet).
When the liquid starts bubbling, lower the heat to medium. Add 250g short pasta and stir. Top with broccoli florets, pushing them into the liquid.
Place a lid on the pot and cook for 5 minutes.
Remove the lid. Cook for another 3 to 4 minutes, stirring frequently, until the pasta is almost cooked through and most of the liquid has been absorbed.
Stir through half the cheese (if using). Adjust salt and pepper to taste.
Top with the remaining cheese, put the lid back on. Leave for 1 minute until the cheese is melted and the pasta is perfectly cooked.