In a large bowl, whisk together 3/4 cups of the flour, garlic powder and smoked paprika; set aside.
In a separate large bowl, beat the egg yolk then stir in the beer, butter, lime juice, salt and pepper. Mix into the flour and spices until just incorporated. The batter should be a similar consistency to pancake batter. Add more or less beer to achieve the appropriate thickness. Allow the batter to stand for 1 hour.
Heat a couple inches of oil to 350 degrees in a heavy sauce pan or Dutch oven. Meanwhile, whip the egg white until stiff peaks form, then fold into the beer batter. Place the onion slices into a plastic zipper bag with the remaining 3/4 cup flour. Shake to coat the onions.
Remove flour-coated onions one at a time then dip into the beer batter. Transfer to the hot oil (in batches so to not over-crowd) and fry until golden, turning halfway to evenly brown each side. Raise oil temperature back to 350 degrees in between batches. Drain on a baking sheet lined with paper towels and serve with your favorite dipping sauce.
Source: Methods and ingredients adapted from multiple sources.