Preheat the oven to 450 degrees. Spray a baking sheet slightly with oil and set aside.
Place Ritz crackers into a food processor and process into crumbs, or place in a sealable plastic bag and crush with a rolling pin. Transfer to a shallow bowl, add cayenne, and set aside. In another bowl, combine buttermilk, 2 tablespoons of flour, salt and pepper and set aside. Slice onions into 1/2-inch circles and separate into rings.
Place the remaining flour in a sealable plastic bag, then add onions, and shake to coat. Dip onions 1 at a time into the buttermilk mixture, then into cracker crumbs and place on baking sheet.
Spray cooking spray evenly over rings and bake for 20 minutes, or until coating is crisp. Season with salt and serve immediately.
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