1Bring a large pot of lightly salted water to a boil. Add broccoli and cauliflower and cook uncovered until tender yet firm to the bite, 2 to 3 minutes. Drain in a colander and immediately immerse in ice water for several minutes to stop the cooking process. Drain and transfer broccoli-cauliflower to a baking dish.
2Melt butter in a saucepan over medium heat; add flour and stir until browned and bubbling, 3 to 4 minutes. Whisk half-and-half and Dijon mustard into butter-flour mixture; bring to a boil, reduce heat to medium-low, and simmer until cream sauce is thickened, about 2 minutes.
3Stir 2/3 cup Cheddar cheese, Parmesan cheese, and paprika into cream sauce; cook and stir until cheeses are melted. Season sauce with salt and pepper. Pour sauce over broccoli-cauliflower mixture and top with 3 tablespoons Cheddar cheese and bread crumbs.
4Bake in the preheated oven until topping is lightly browned, 15 to 20 minutes.
Footnotes
Cook's Notes:
Any sharp cheese can be substituted for the Cheddar. Romano cheese can be substituted for the Parmesan cheese.