Make batter and place remaining flour in shallow dish: Whisk together 1 cup flour, the salt, white pepper, and baking powder in a bowl. Whisk in beer and ice water until combined. Place remaining cup flour in a shallow dish.
Preheat oven and heat oil: Preheat oven to 200°F, with a baking sheet on middle rack. Heat 3 inches of oil to 375°F in a medium pot over medium high.
Dredge onions in flour and dip in batter: Dredge onions in flour, turning to coat; tap off excess. Working in batches (about 8 at a time), dip onions in batter, shaking off excess.
Cook onion rings: Carefully add to hot oil. Cook until golden brown, 2 to 3 minutes.
Drain, season, and keep warm while cooking reminaing onions: Transfer to paper towels to drain. Sprinkle with salt. Transfer to baking sheet to keep warm while cooking remaining onions. Adjust heat as necessary to keep oil at a steady temperature. Serve hot. This recipe appears in the cookbook, Martha Stewart's Vegetables .
