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For the Classic Bechamel:
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Heat the milk in a saucepan over medium heat until it is steaming hot (do not let it boil).
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Keep it at this temperature.
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Melt the butter in a heavy-bottomed saucepan over medium-low heat.
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Stir in the flour and cook, stirring constantly, until the paste bubbles, 2 to 3 minutes; dont let it brown.
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Whisk in the hot milk and nutmeg and bring to a boil.
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Cook, whisking constantly, until the sauce thickens, 5 minutes.
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Season with salt and pepper to taste.
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Lower the heat and cook, stirring, for 2 to 3 minutes more.
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For the Root Vegetable Gratin:
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Preheat the oven to 350F.
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Grease a 12- to 14-inch round baking dish or a 13 x 9-inch rectangular baking dish with the butter.
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Pour the bechamel into a saucepan and bring it to a simmer over low heat.
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Remove the pan from the heat, add the whole dried chiles, and steep for about 10 minutes.
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Remove and discard the chiles.
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Arrange half of the russet potato slices in a single layer on the bottom of the prepared baking dish.
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Top with a third of the red pepper strips.
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Season with salt and pepper to taste.
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Spread 1 1/2 cups of the bechamel evenly over the potatoes and red pepper strips.
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Sprinkle with 1 cup of the cheddar.
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Arrange the sweet potato slices on top, slightly overlapping, in a spiral pattern.
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Season with salt and pepper, and top with another third of the red pepper strips.
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Again top with 1 1/2 cups bechamel followed by 1 cup cheddar.
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Add the slices of rutabaga, slightly overlapping in a spiral pattern, and strew with the remaining red pepper strips.
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Add 1 1/2 cups bechamel followed by 1 cup cheddar.
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For the final layer, arrange the remaining slices of russet potato on top, slightly overlapping, in a spiral pattern.
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Season with salt and pepper.
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Spread the remaining 1 1/2 cups bechamel and 1 cup cheddar on top.
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Cover the dish with aluminum foil and bake for 1 1/4 hours.
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Remove the foil and bake until the top of the gratin is bubbly and nicely browned, about 20 minutes.
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A knife inserted in the center of the gratin should easily pierce the fully cooked, soft root vegetables.
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Serve piping hot.
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Variations:
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To lighten this dish, make a cornstarch/water slurry, stir it into chicken broth, and simmer until it achieves a bechamel-like consistency.
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Use in place of bechamel.
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Omit the chiles and/or roasted red bell pepper.
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Substitute turnips for the rutabaga.
