Peel the onions, slice them into 1/2-inch thick rings, and carefully separate the layers.
In a large mixing bowl, whisk together the all-purpose flour, paprika, garlic powder, salt, and black pepper.
Gradually pour the cold beer into the dry ingredients, whisking gently until just combined. A few lumps are fine.
Heat the vegetable oil in a heavy-bottomed pot or deep fryer to 375 degrees Fahrenheit.
Dip each onion ring into the batter, allowing the excess to drip off, and carefully lower it into the hot oil.
Fry the rings in small batches for 2 to 3 minutes per side until golden brown and crispy.
Remove from oil, drain on a wire rack or paper towels, and season immediately with additional salt. Serve hot with ketchup.