In a large bowl, whisk together 1 1/2 cups of flour with the paprika, garlic powder, salt and pepper. Whisk in the beer until the mixture is well combined. Let the batter rest at room temperature for 10 minutes.
While the batter rests, cut the tip off of the stem side of the onions then remove the peel. Slice the onions horizontally into 1/2-inch-thick rings and toss them with the remaining 1/2 cup of flour.
Add the vegetable oil to a large, heavy-bottomed pot (Dutch oven) to a depth of 2 inches and heat it over medium-high heat until a deep-fry thermometer reaches 375°F.
Working in batches, dip the onion rings into the prepared batter, shaking off any excess, then immediately drop them into the hot oil. Be careful not to overcrowd the pot. Allow the onions to cook in the oil, flipping them once to guarantee even browning, for a total of about 3 minutes. Remove the onions with a slotted spoon and transfer them to a paper towel-lined plate. Immediately season them with salt. Repeat the coating and frying process, returning the oil to 375°F between batches, with the remaining onions.