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 drizzle with a little olive oil. Bake for 10 to 15 minutes, or until coating is crisp. Season with salt and serve with spicy ketchup or BBQ sauce.