Bring a large pot of salted water to a boil. Cook pasta according to package directions, adding broccoli during the last 2 minutes. Drain and set aside.

In a saucepan over medium heat, melt butter. Add garlic and cook until fragrant, about 30 seconds.

Whisk in flour and cook for 1 minute, stirring constantly.

Slowly whisk in milk and cream. Cook until the sauce thickens, about 3–4 minutes.

Reduce heat and stir in cheddar and parmesan until melted and smooth. Season with salt and pepper.

Add cooked pasta and broccoli to the sauce and toss until evenly coated. Serve warm.