In a large deep skillet or pot, combine the dry fettuccine pasta, broccoli florets, minced garlic, vegetable broth, and whole milk.
Bring the mixture to a boil over medium-high heat, stirring occasionally to prevent the noodles from sticking.
Once boiling, reduce the heat to medium and simmer uncovered, stirring frequently, until the pasta is al dente and the broccoli is tender, about 10 to 12 minutes. If the liquid reduces too quickly before the pasta is cooked, add a little more broth or water as needed.
Remove the pot from heat and stir in the unsalted butter until melted and combined.
Add the freshly grated Parmesan cheese, salt, black pepper, and crushed red pepper flakes. Stir well until the cheese is fully melted and the sauce becomes creamy.
Taste and adjust seasoning if necessary.
Serve immediately, garnished with additional Parmesan cheese if desired.