Preheat oven to 200 degrees F and adjust oven rack to middle position. In a Dutch oven, heat oil to 350 degrees F over medium-high heat. In a zipper-lock bag, place onion rounds, 2 cups beer, vinegar and salt and pepper. Zip bag tight and refrigerate at least 30 minutes or up to 2 hours. NOTE: Do not refrigerate onion rounds longer than 2 hours or they will become soft and too saturated to crisp properly. In a large bowl, combine flour, cornstarch, baking powder and season to taste using salt and pepper. Slowly whisk in 3/4 cup beer until just combined, some lumps will remain. Whisk in remaining beer as needed, 1 tablespoon at a time, until batter falls from whisk in steady stream and leaves faint trail across surface of batter. Set batter aside. Line a baking sheet with paper towels. Remove onions from refrigerator and discard liquid. Pat onion rounds dry with paper towels and separate into rings. Transfer one-third portion of rings to batter, turning to coat well. Carefully transfer battered rings to oil, one at a time, and fry about 5 minutes or until rings are golden brown and crisp, flipping halfway through frying. Drain rings on baking sheet and season to taste with salt and pepper. Place in oven to keep warm. Return oil to 350 degrees F and repeat with remaining onion rings. Serve immediately.