Line a large, rimmed baking sheet with paper towels and heat the oven to 175 F or 200 F.
Separate the sliced onions into rings.
Heat about 2 to 3 inches of vegetable oil to 365 F in a deep fryer or in a deep, heavy pan over medium-high heat.
Combine the flour, salt, pepper, and baking powder in a mixing bowl; whisk to blend.
In a separate bowl, whisk the eggs with the milk until well blended. Add the egg mixture to the dry ingredients and stir to blend.
Dip several onion rings into the batter to coat, then drop them in the hot oil. Avoid overcrowding as it will lower the temperature. Fry the onion rings for about 2 minutes or until golden brown, turning to brown both sides.
Use a slotted spoon to transfer the onion rings to the paper towel-lined pan and place them in the warm oven. They will stay crisp for 20 to 25 minutes. Repeat with the remaining onion rings.