Preheat the oven to 375°F., and butter a 2-quart ovenproof casserole dish.
Bring a large saucepan of lightly salted water to a boil, and toss in the bucatini. Boil until just slightly firm (al dente), drain in a colander (do not rinse), and set aside momentarily.
Melt the butter in a large saucepan over medium heat, stir in the flour to form a smooth paste (roux), and cook for about 1 minute. Pour in the milk, whisking constantly, and bring to a boil. Remove from the heat, season with salt and white pepper, and add the nutmeg and thyme. Stir in the cheddar cheese a bit at a time until incorporated and smooth.
Add the bucatini to the cheese sauce, stirring gently to coat, and pour into the prepared casserole dish. Sprinkle the top evenly with Parmesan cheese, and bake for 10 minutes. Remove the casserole from the oven, and place under the broiler until bubbly and golden brown. (Watch carefully to prevent the top from burning.)
Sprinkle with paprika, and serve hot.
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