How to Make It
Preheat oven to 450°F. Toss together broccoli florets, minced garlic, olive oil, 1 tsp. kosher salt, and 1/2 tsp. black pepper in a large bowl. Spread mixture in 1 layer on a rimmed baking sheet; bake in preheated oven until lightly browned, 20 minutes.
Reduce oven temperature to 350°F. Prepare pasta according to package directions for al dente.
Melt butter in a large saucepan over medium. Add next 6 ingredients; cook, stirring, 30 seconds. Add flour, and cook, stirring, until golden, 2 minutes. Gradually whisk in milk and cream. Bring to a boil, whisking occasionally. Reduce heat to medium-low; simmer, whisking, until slightly thickened, 5 minutes. Stir in Worcestershire sauce. Remove from heat; stir in 3/4 cup each of shredded Cheddar cheeses until melted. (Reserve remaining 1/4 cup each of shredded cheeses.) Stir in pasta, roasted broccoli, and diced cheeses; pour into a lightly greased 13- x 9-inch (3-quart) baking dish.
Bake on a rimmed baking sheet in preheated oven until bubbly and golden, 30 minutes. Remove from oven; increase oven temperature to broil. Sprinkle with reserved shredded cheeses; broil 6 inches from heat until cheeses are melted and golden, about 2 minutes. Remove from oven; cool slightly on a wire rack, about 15 minutes.
Make it ahead: Prepare through Step 2 up to 1 day in advance; cover and refrigerate. Bring to room temperature before proceeding with Step 3.