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SPECIAL EQUIPMENT SUGGESTED: A food processor is useful for slicing and grating; and 8-quart covered kettle.
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A heavy-bottomed 3-quart saucepan, for the sauce.
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A buttered 6-quart baking dish about 3 inches deep, for the final dish.
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THE POTATOES: Have ready the kettle containing 4 cups of cold water.
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Peel the potatoes and slice them 1/4 inch thick, dropping them into the cold water to cover as you do so.
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Cover the kettle, and bring to the boil.
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Uncover and boil slowly for 3 to 4 minutes, until barely cooked through eat several slices to check.
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Drain, cover the kettle again for 3 to 4 minutes to firm up the potato slices, then uncover.
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THE GARLIC AND MUSTARD SAUCE: Make the classic white sauce; cook the butter and flour together in the saucepan until they foam and froth for 2 minutes without coloring.
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Off heat pour in half the hot milk; whisk vigorously to blend as you pour in the rest; simmer for 3 minutes, stirring.
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Remove from heat and whisk in the seasonings; bring to the simmer again; taste carefully, and add additional seasonings to taste.
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ASSEMBLING: Spoon a 1/16-inch layer of sauce on the bottom of the buttered baking dish.
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Set aside 3 cups of the sauce and 1 cup of the cheese for the topping.
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Now, to arrange everything in 4 layers, start with a quart of the potatoes, then a quarter of the ham, follow by a third of the sauce and sprinkle on a third of the cheese.
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Continue in layers, finishing the final layer with the remaining potatoes and ham; spread on the reserved 3 cups of sauce to cover completely, then the last of the cheese.
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AHEAD OF TIME NOTE: May be prepared a day in advance, cover when cool and refrigerate.
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An hour or so before you plan to serve, preheat the oven to 375F (190C).
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Bake in the upper third level just until the potatoes are bubbling hot and the top has browned nicely.
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About 45 minutes.
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AHEAD OF TIME NOTE: May be kept warm uncovered on a hot tray but be sure not to overheat or the potatoes and ham will dry out.