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 3750F. 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.To Roast Peppers: 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.