Begin by bringing a large pot of salted water to a rolling boil. Add pasta and cook until al dente, about 8-10 minutes. Reserve ½ cup pasta water, then drain and set aside.

Prepare a bowl of ice water. In a separate pot, boil water and add broccoli florets. Blanch for 1-2 minutes until bright green. Transfer to ice water, then drain.

In a skillet over medium heat, melt butter. Add minced garlic and sauté for 1-2 minutes until fragrant.

Sprinkle flour into the skillet and stir continuously for about 1 minute to form a roux.

Gradually whisk in milk or cream, stirring until the mixture thickens to a silky consistency.

Reduce heat to low and stir in grated cheddar cheese until melted and incorporated into the sauce.

Combine cooked pasta and blanched broccoli with the cheese sauce, stirring gently. Adjust thickness with reserved pasta water as needed.

Serve immediately, garnished with fresh parsley if desired.