Preheat oven to 425°F and set the oven rack to the middle position. Spray a 2-quart (11x7-inch) casserole dish with nonstick cooking spray.
Tear each slice of bread into 4 pieces.
3 slices sandwich bread
Place the bread, butter, salt, and pepper in a food processor fitted with a metal blade. Process until coarse crumbs form, about ten 1-second pulses. Set aside.
2 tablespoons unsalted butter, ¼ teaspoon table salt, ⅛ teaspoon freshly ground black pepper
Trim the cauliflower and broccoli into ¾-inch florets. If using broccoli stalks, use only ½-inch of stalk next to the floret.
1 head cauliflower, 1 head broccoli
Fill a Dutch oven or stockpot two-thirds full with water. Add 1 tablespoon of salt and bring the water to a boil. Stir the boiling water and add the cauliflower and broccoli. Cook until the vegetables have a slight bite, 3-4 minutes, and drain.
1 tablespoon table salt
Heat a large skillet over medium heat. Add butter and cook just until foaming subsides.
2 tablespoons unsalted butter
Add the onion and cook until softened and translucent, 2-3 minutes.
¼ yellow onion
Add the garlic and cook for 30 seconds.
1 clove garlic
Sprinkle the flour over the onion/garlic mixture; stir and cook for about 1 minute.
1½ tablespoons all-purpose flour
Reduce the heat to medium-low and whisk in the cream and broth (or wine). While stirring, bring to a boil.
1¼ cups heavy cream, ¼ cup low-sodium chicken broth
Reduce heat to low and add nutmeg, dry mustard, red pepper flakes, and black pepper. Cook (and stir) just until the mixture has thickened a little. Add salt to taste if needed.
2 pinches freshly grated nutmeg, 1 teaspoon dry mustard powder, 1 teaspoon crushed red pepper flakes, ⅛ teaspoon freshly ground black pepper
Add both cheeses and stir until cheese is melted.
½ cup freshly grated Parmesan cheese, 1 cup freshly shredded sharp cheddar cheese
Remove from the heat and add the cauliflower and broccoli; stir gently to coat the vegetables
Transfer cauliflower/broccoli mixture to the prepared dish and sprinkle with the breadcrumb topping.
Bake at 425°F for 15-20 minutes or until the sauce bubbles around the edges and the top is golden brown. Serve immediately.