Combine buttermilk, flour, cayenne and salt in a large bowl until smooth. Soak the onion rings in the batter for 2 hours in the refrigerator. Using side burner. Heat oil in a large saucepan to 375 degrees F. In batches, remove onion rings from batter and dredge in the seasoned flour mixture. Fry for 3 to 4 minutes or until golden brown. Drain on paper towels and season immediately with salt.
For the aioli: place all ingredients in a blender and blend until smooth. Season with cayenne and salt.