Separate the onion rounds into individual rings. Place in a gallon-sized zipper-lock freezer bag and put them in the freezer until completely frozen, at least 1 hour (they can stay in the freezer for up to 1 month).

When ready to fry, remove the onion rings from the freezer bag, transfer to a colander, and thaw under tepid running water. Transfer to a rimmed baking sheet lined with a clean kitchen towel or several layers of paper towels and dry the rings thoroughly. Carefully peel off the inner papery membrane from each ring and discard (the rings will be very floppy). Set aside.

Preheat the oil to 375°F in a large pan. Put a rack on a rimmed baking sheet and place paper towels on top.

Combine the flour, cornstarch, baking powder, baking soda, and paprika in a medium bowl and whisk together. Combine the beer and vodka in a small bowl. 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.

Dust the onion rings with flour and shake off excess. Dip one onion ring in the batter then lift it out, letting the excess batter drip off, then slowly lower it into the oil. Repeat with the remaining onion rings, being careful not to over crowd the pan (fry in batches). Flip the rings halfway through cooking, until they are deep golden brown, about 4 minutes. Transfer the rings to the baking sheet and sprinkle with salt. The fried rings can be kept hot in a 200°F oven while you fry the remaining rings. Serve immediately.