Preheat broiler. Carefully cut a lengthwise slit in each chile and stuff with some Cheddar. Combine flour, salt, and pepper and dredge chiles. In a large saucepan, heat 1/2 inch shortening to 375°F. on a deep-fat thermometer. Fold yolks into egg whites. Working with 2 chiles at a time, using a slotted spoon, dip chiles into eggs and fry, turning occasionally, until golden, no more than a couple of minutes. With a slotted spoon transfer chiles (careful they are delicate!) to paper towels to drain. Arrange chiles on a flameproof plate and sprinkle with sharp Cheddar. Broil chiles just long enough to melt cheese and serve immediately, accompanied by salsa if desired. : Using a long-handled fork, char peppers over an open flame or on a rack set over an electric burner, turning, until skins are blackened, 4 to 6 minutes. (Alternatively, broil peppers on rack of a broiler pan under a preheat broiler about 2 inches from heat,turning every 5 minutes, 15 to 20 minutes, or until skins are blistered and charred.) Transfer peppers to a bowl and let stand, covered, until cool enough to handle. Keeping peppers whole, peel them, starting at blossom end. Cut off tops and discard seeds and ribs.