Fill a fryer or large Dutch oven with 2 inches vegetable oil; heat to 330 degrees F to 340 degrees F. Prepare the batter: Whisk the all-purpose flour, rice flour, parmesan, mustard powder, paprika, garlic powder and 2 tablespoons salt in a large bowl. Whisk the buttermilk, beer and dijon mustard in a separate large bowl. Add all but 1 cup of the wet ingredients to the dry ingredients and whisk to make a smooth batter, similar to a pancake batter.
Test 1 onion ring: Dip in the batter and fry until golden brown, about 2 minutes. If the batter is still not cooked through, then it is probably too thick; add a splash more of the wet ingredients to the batter. (You may also need to add more of the wet ingredients to the batter as it sits.)
Working in batches, dip the remaining onion rings in the batter and fry until golden brown, about 2 minutes. Remove with a slotted spoon and transfer to a rack. Immediately sprinkle with more parmesan.