2 large yellow onions, sliced into ½-inch thick rings
6 tbsp. vegetable oil
Adjust oven racks to lower- and upper-middle positions. Preheat the oven to 450F. Place ¼ cup of the flour in a shallow baking dish. Beat the egg and buttermilk together in a bowl. Whisk the remaining flour, cayenne, salt and pepper into the buttermilk mixture. Combine the saltines and potato chips in a food processor and pulse until finely ground. Place half of the crumb mixture in a second shallow baking dish; reserve the other half.
Working one at a time, dredge each onion ring in flour, shaking off the excess. Dip the onion rings in the buttermilk mixture, allowing the excess to drip back into the bowl, and then dredge in the crumb coating, turning to coat evenly. When the crumb mixture is low, add the reserved crumb mixture to the dish to coat the remaining onion rings. Transfer the coated rings to a large plate or platter.
Pour 3 tablespoons of the oil onto each of 2 rimmed baking sheets. Place the baking sheets in the oven and heat just until smoking, about 8 minutes. Tilt the heated sheets to coat evenly with the oil.
Lay the onion rings out in a single layer on the oiled baking sheets. Bake, flipping the onion rings and rotating the pans halfway through baking, until golden brown on both sides, about 15 minutes total. Transfer to a paper towel-lined rack briefly before serving.