Cook the spaghetti in a large pot of boiling water according to package directions, omitting any salt.
Add the broccoli florets to the pot during the last 3 minutes of cooking.
Drain the pasta and broccoli, but do not rinse. Return the mixture to the hot pot.
To the pot with the pasta and broccoli, add the drained diced tomatoes, rinsed cannellini beans, tomato paste, minced garlic, salt, and pepper.
Stir gently to combine all .
Heat the mixture over medium heat for 2-3 minutes, or until everything is heated through.
Stir in the fresh parsley, then serve immediately, sprinkled generously with vegan Parmesan cheese.
After cooking the pasta and broccoli, drain it but do not rinse. The starchy coating that remains on the pasta helps the sauce cling to every noodle.
Add a pinch of red pepper flakes along with the garlic for a gentle kick of heat.