Slice both onions into 1/4-inch thick rings, then separate them into individual rings. Pat them completely dry using paper towels, pressing gently to remove all surface moisture. This step is crucial because water prevents the batter from adhering and creates steam during frying.
In a large mixing bowl, whisk together flour, cornstarch, salt, black pepper, cayenne pepper, garlic powder, and paprika until well combined. Add the egg white to your ice-cold water and whisk together until frothy and light. This creates the perfect batter base.
Pour the wet ingredients into the dry mixture and stir until just combined—the batter should be thick but pourable, similar to pancake batter consistency. Don't overmix or the gluten will develop, making your rings tough instead of delicate. Let it rest for exactly two minutes.
Heat 2 cups of vegetable oil in a deep skillet or Dutch oven to 365°F, checking temperature with a reliable thermometer. Crispy game day onion rings require precise heat—too hot and they'll burn outside while staying raw inside; too cool and they'll absorb oil and become greasy instead of crunchy.
Working in batches of 6-8 rings, dip each onion ring into the batter, coating completely on all sides with a quick turn. Carefully place into the hot oil, frying for 2-3 minutes until golden brown on the first side, then flip gently and cook another minute until deep golden.
Remove rings with a slotted spoon and drain on paper towels for one minute before transferring to a wire rack. This prevents moisture from condensing underneath, keeping them crispy much longer. Season immediately with additional salt if desired.
Repeat batches until all onion rings are cooked, allowing oil temperature to return to 365°F between each batch. Serve immediately while they're at peak crispiness, or hold in a 200°F oven for up to 15 minutes.