Preheat oven to 450°F. Toss together broccoli, garlic, olive oil, 1 tsp. kosher salt, and 1/2 tsp. black pepper in a large bowl. Spread broccoli mixture in a single layer on a rimmed baking sheet, and bake in preheated oven until lightly browned, about 20 minutes.

Meanwhile, prepare pasta according to package directions for al dente.

Melt butter in a large saucepan over medium. Add onion, mustard, salt, black pepper, nutmeg, and cayenne; cook, stirring constantly, until fragrant, about 30 seconds. Add flour, and cook, stirring constantly, until golden brown and smooth, about 2 minutes. Gradually whisk in milk and cream, and bring to a boil, whisking occasionally. Reduce heat to medium-low, and simmer, whisking constantly, until slightly thickened and mixture coats a spoon, about 5 minutes. Stir in Worcestershire sauce. Remove from heat, and stir in remaining 3/4 cup each of shredded Cheddar cheeses until melted. Stir in roasted broccoli, cooked pasta, and diced cheeses; pour into a lightly greased 13- x 9-inch (3-quart) ceramic baking dish.

Bake on a rimmed baking sheet in preheated oven until bubbly and golden, about 30 minutes. Remove from oven, and increase oven temperature to broil. Sprinkle casserole with reserved shredded Cheddar cheeses, and broil 6 inches from heat until cheese is melted and golden brown, about 2 minutes. Remove from oven, and cool slightly on a wire rack, about 15 minutes. Serve immediately.