In a large pot, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1-2 minutes until fragrant, being careful not to burn it.
Add the pasta to the pot along with the vegetable broth and bring to a simmer. Stir occasionally to prevent sticking.
After 5 minutes of cooking, add the broccoli florets to the pot. Continue to cook until the pasta is al dente and the broccoli is tender, about another 5-7 minutes.
Once the pasta is cooked, reduce the heat to low. Stir in the heavy cream and Parmesan cheese until fully incorporated, creating a creamy sauce.
Add the lemon zest, and season with salt, black pepper, and crushed red pepper flakes if using. Stir until everything is well combined.
Remove from heat and let it sit for a couple of minutes to thicken slightly.
Serve warm, garnished with fresh basil leaves and an extra sprinkle of Parmesan if desired.
Notes
For a dairy-free option, use coconut cream and nutritional yeast.