Cut onion 1/2 inch thick, separate into rings and soak in buttermilk mixed with 1/4 tsp cayenne pepper for 1 hour.
Mix 1/2 cup flour, salt, pepper, cayenne and garlic. Set aside. In a medium-sized bowl, combine beer and remaining flour. Mix thoroughly.
In a large, deep pot, heat oil to 350°F. Remove onion rings from buttermilk, shake off excess, dredge in flour, then dip in beer batter. Drop some onion rings into oil and repeat process, being sure not to crowd rings, as they will stick together. When golden, remove and let drain on paper towels.