Preheat your oven to 375°F. Grease a 9x13-inch baking dish.
In a large pot of boiling salted water, blanch the broccoli and cauliflower florets for 3-4 minutes, or until just tender. Drain and set aside.
4 cups broccoli florets, 4 cups cauliflower florets
In a large saucepan, melt the butter over medium heat. Add the chopped onion and sauté until softened, about 5 minutes. Add the minced garlic and cook for another minute. Stir in the flour and cook for 1-2 minutes until lightly browned.
2 tablespoons unsalted butter, 1 small onion, 2 cloves garlic, ¼ cup all-purpose flour
Gradually whisk in the milk and heavy cream and cook until the sauce thickens, about 5-7 minutes. Stir in the shredded cheddar cheese, grated Parmesan cheese, Dijon mustard, salt, and pepper until the cheese is melted and the sauce is smooth.
1 cup milk, 1 cup heavy cream, 1 cup shredded cheddar cheese, ½ cup grated parmesan cheese, 1 teaspoon Dijon mustard, ¼ teaspoon smoked paprika, Salt and pepper to taste
Place the blanched broccoli and cauliflower florets in the prepared baking dish. Pour the cheese sauce over the vegetables and stir to coat evenly.