Make the crisp: Brush a baking sheet well with some of the oil. In a food processor fitted with the 2-millimeter slicing disk or with a hand-held slicing device slice thin the potato on the diagonal (cut one end of the potato on the diagonal to facilitate this) and arrange the slices immediately in one layer on the sheet. Brush the slices with the remaining oil, sprinkle them with salt to taste, and bake them in the middle of a preheated 400 deg. F. oven for 12 to 15 minutes, or until they are golden brown. Transfer the crisps while they are still warm with a metal spatula to a rack and let them cool. The crisps may be made several days in advance and kept in a plastic bag at room temperature.

Make the puree: Peel the potatoes, quarter them lengthwise, and cut them into 1-inch pieces. Reserving 3 of the garlic cloves for the ragout, in a steamer set over boiling water steam the remaining garlic cloves with the potatoes, covered, for 12 to 15 minutes, or until the potatoes are very tender. Force the steamed garlic and the potatoes through a ricer or food mill fitted with the medium disk into a large bowl, stir in the butter, the milk, and salt and pepper to taste, and keep the puree warm, covered. The puree may be made 1 day in advance, kept covered and chilled, and reheated.

Make the ragout:: In a large heavy skillet heat the oil over moderately high heat until it is hot but not smoking and in it saute the mushrooms with the reserved garlic cloves, minced, and salt and pepper to taste for 5 minutes, or until the mushrooms are softened and any liquid they give off is evaporated. Add the Sherry and boil the mixture until almost all the liquid is evaporated. Add the broth and the soy sauce and bring the mixture to a boil. Stir the cornstarch mixture, stir it into the sauce, and simmer the ragout, stirring occasionally, for 2 minutes. Stir in the parsley. The ragout may be made 1 day in advance, kept covered and chilled, and reheated.

Divide the puree among 8 heated small plates, mounding it, arrange 3 crisps decoratively in each mound, and spoon the ragout over and around the puree. Serves 8