Cook the pasta according to package instructions in a large pot of salted boiling water. Add the broccoli florets during the last 3 minutes of cooking. Drain and set aside.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant but not browned.
Pour in the vegetable broth and almond milk, stirring to combine. Bring the mixture to a simmer.
If using, stir in the nutritional yeast, salt, pepper, and red pepper flakes. Let the sauce simmer for about 5 minutes, allowing it to thicken slightly.
Add the cooked pasta and broccoli back into the pot, tossing to coat everything in the creamy sauce. Cook for an additional 2-3 minutes until heated through.
Serve hot, garnished with fresh parsley.