Pour oil into a wide, deep pot to a depth of 2 inches and heat over medium-high heat until temperature reaches 365 degrees F.
Whisk together the flour and prosecco in a large bowl until batter is smooth.
Season with salt and pepper.
Slice onions into 1-inch-thick rounds, then separate into rings.
Working in small batches, coat onion rings in batter, then use a fork to transfer rings one at a time to hot oil and deep-fry, turning often, until golden and crisp, 2-3 minutes per batch.
Transfer onion rings with a slotted spoon to paper towels to drain.