Heat oil in a large pot and add garlic and onions and cook on a medium flame for 2-3 minutes, until the onions are translucent. Turn heat to high and add the corn kernels, zucchini, and mushrooms. Cook, stirring occasionally for 2-3 minutes.
Next, add the vegetable broth, crushed tomatoes and tomato paste and let cook on high heat. When the liquid starts boiling, reduce heat and add the broccoli, red bell pepper, pasta, herbs, pepper flakes, salt and black pepper. Give it a stir, place the lid on and let it cook on a slow flame for 4-5 minutes.
Take the lid off and cook for another 2-3 minutes, stirring frequently till the pasta is done and all the liquid is absorbed.
Stir in half the shredded cheese and taste to check for the seasonings. Add more salt or pepper if required.
Sprinkle the remaining cheese on top, cover with the lid and take off heat. The cheese will melt in the residual heat.
Garnish with the parsley and shredded parmesan and serve hot.