Step 1

Preheat oven to 375°F. Butter a shallow 3-quart baking dish. Arrange cauliflower and broccoli in the prepared dish.

Step 2

Melt butter in a medium saucepan over medium heat. Add flour and cook, stirring, 2 minutes (do not let it darken). Slowly whisk in milk. Simmer, whisking occasionally, until slightly thickened, 3 to 4 minutes. Remove from heat and stir in nutmeg and 1 1/4 cups cheese. Season with salt and pepper. Pour over vegetables. Sprinkle with remaining 3/4 cup cheese.

Step 3

Cover loosely with aluminum foil and bake for 15 minutes. Remove foil; bake until vegetables are tender and the top is golden brown, 20 to 25 minutes. Let stand 10 minutes before serving.