Place onion slices, 2 cups of beer, vinegar, 1/2 teaspoon salt, and 1/2 teaspoon pepper in a large zip-top bag. Refrigerate for at least 30 minutes, but no longer than 2 hours.
In a large bowl, combine flour, cornstarch, baking powder, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Gradually whisk in 3/4 cup of beer just until combined. There will be some lumps. Continue to whisk in beer 1 tablespoon at a time until batter falls from whisk in a steady stream and leaves a faint trail on the surface.
Remove onions from liquid and pat dry with paper towels.
Place one-third of the onion rings in the batter, completely coating them.
Transfer onion rings to oil and fry until golden brown, flipping to brown both sides. Place on paper towel-lined baking sheet and season with salt.