Preheat the oven to 450 degrees F. Grease a large baking dish with butter and add the broccoli and cauliflower. Roast until slightly browned, about 15 minutes.
In a medium saucepan, melt the butter, whisk in the flour and let it cook over medium heat for 3 minutes. Turn the heat off, whisk in the half-and-half, then turn the heat up to high and keep whisking to avoid the flour from clumping. Add the Cheddar, salt and pepper and whisk until the cheese is melted.
Remove the broccoli and cauliflower from the oven and pour the Cheddar mixture over the top. Sprinkle evenly with the breadcrumbs and bake until golden brown, 25 to 30 minutes.