Fill a large pot with water and bring it to a boil. Add pasta and cook according to package instructions until al dente, about 8–10 minutes. Drain and set aside.

In the same pot, melt the butter over medium heat. Add the broccoli florets and sauté for about 3–4 minutes until they soften.

Pour in the milk and stir well. Gradually add in the shredded cheese while stirring until melted and thickened, about 4–5 minutes.

Return the drained pasta to the pot, combining it with the cheese sauce and broccoli mixture. Stir gently for about 2 minutes until well-coated.

Season with salt and pepper to taste, and serve immediately, garnished with extra cheese or fresh herbs if desired.