1. Adjust oven racks to lower-middle and upper-middle positions and heat oven to 450 degrees. Place 1/4 cup flour in shallow baking dish. Beat egg and buttermilk together in medium bowl.Whisk remaining 1/4 cup flour, cayenne, 1/2 teaspoon salt, and 1/4 teaspoon pepper into buttermilk mixture. Pulse saltines and chips together in food processor until finely ground and place in separate baking dish.
2. Pull apart rings in each roundm, discarding any that are less than 2 inches in diameter. Working one at a time, dredge each onion ring in flour, shaking off excess. Dip in buttermilk mixgture,a llowing excess to drip back into bowl,then drop into crumb coating, turning ring to coat evenly. Transfer to large plate and repeat with remaining onion rings.
3. Pour 3 tablespoons oil onto each of two rimmed baking sheets. Place in oven and heat until just smoking, about 8 minutes. Carefuilly tilt heated sheets to coat evenly with oil, then arrange onion rings on sheets. Bake, flipping onion rings and switching and rotating position of baking s heets halfway through baking, until go lden brown on both sides, aobut 15 minutes. Transfer onion rings to paper towl-lined plates to drain briefly. Serve immediately.
