Slowly add the beer mixture to the flour mixture, whisking constantly until the batter has texture of thick paint (you may not need all of the beer). The batter should leave a trail if you drip it back into the bowl off the whisk. Do not overmix; a few small lumps are OK. Dip one onion ring in the batter, making sure that all surfaces are coated, lift it out, letting the excess batter drip off, and add it to the hot oil by slowly lowering it in with your fingers until just one side is sticking out, then dropping it in. Repeat until half of the rings are in the oil. Fry, flipping the rings halfway through cooking, until they are deep golden brown, about 4 minutes. Transfer the rings to a large mixing bowl lined with paper towels and toss while sprinkling salt over them. The fried rings can be placed on a rack on a rimmed baking sheet and kept hot in a 200°F oven while you fry the remaining rings. Serve the rings immediately.