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Preheat the oven to 400º. Butter a baking dish and set aside.
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Bring a pot of water to a boil and add a large pinch of salt. Separately blanch the cauliflower and broccoli florets until crisp yet tender. Drain and pat dry.
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Arrange the cauliflower and broccoli florets, stems down, in the buttered gratin dish.
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Make the sauce: Heat a saucepan over medium heat and add the butter. Once the butter has melted, add the flour to make a roux. Cook the mixture, stirring constantly with a whisk for about 1 minute.
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Gradually whisk the milk into the flour mixture. Add the thyme and bay leaf. Bring to a boil over medium-high heat, whisking to prevent lumps. Reduce heat to low, and simmer, whisking occasionally, until the sauce is thick, about 10 minutes.
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Remove the bay leaf and thyme. Season the sauce with salt, pepper, nutmeg and cayenne to taste. Whisk in the cheese and pour the cheese sauce over the cauliflower and broccoli.
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Make the topping: For the topping, stir the melted butter into the bread crumbs and parsley. Sprinkle on the top of the gratin.
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Bake until the top of the gratin is golden brown and the sauce bubbly, 20 to 25 minutes. Allow to rest for 5 minutes before serving.
