Warm the olive oil or butter in a large pot over medium heat and gently cook the minced garlic for about 1-2 minutes until fragrant.
Pour in the pasta and broth, bring the mixture to a gentle boil, then lower the heat to maintain a simmer.
About halfway through the pasta cooking time, fold in the broccoli florets to soften alongside the pasta.
When the pasta is cooked through and tender, stir in the heavy cream and Parmesan cheese until everything is well combined and creamy.
Season the dish with salt and pepper to your liking, then serve immediately while warm.