In a large pot of salted boiling water, add pasta and broccoli florets. Cook until the pasta is al dente, about 8-10 minutes. Drain and set aside.

In the same pot, melt butter over medium heat. Add minced garlic and sauté for about 1-2 minutes until fragrant.

Whisk in all-purpose flour, stirring constantly for 1-2 minutes to form a roux.

Gradually pour in milk and heavy cream, whisking continuously. Cook over medium heat until the mixture thickens, about 5 minutes.

Stir in shredded cheddar cheese and grated Parmesan cheese. Keep stirring until melted and creamy.

Toss the cooked pasta and broccoli into the cheese sauce until evenly coated. Serve warm.