Peel the 3 large onions and cut into 1/4-inch slices. Carefully separate the slices into individual rings and set aside.
In a medium bowl, combine the 2 cups all-purpose flour, 1 1/4 teaspoons baking powder, 1 teaspoon onion powder, 1 1/2 teaspoons garlic powder, 1 teaspoon paprika, and 1 1/4 teaspoons salt. Mix until uniform.
Divide the flour mixture into two bowls: one bowl for dry dredging and one bowl to make the batter.
Place the 1 1/2 cups panko bread crumbs in a shallow dish and set aside.
In the bowl reserved for the batter, add the 2 eggs and 1 1/2 cups milk. Whisk into the flour mixture until a smooth batter forms. Add more milk only if needed to reach a batter that will coat the rings.
Working a few rings at a time, dredge each onion ring in the dry flour mixture so it is evenly coated. Shake off excess flour.
Dip each floured ring into the batter, letting excess batter drip back into the bowl, then transfer the ring to the panko. Press panko onto both sides so each ring is fully coated. Place coated rings on a wire rack while you finish coating the rest.
Pour about 5 cups oil (or enough oil to fully submerge the rings) into a deep fryer or a large, heavy pot. Heat the oil to 365°F (185°C).
Fry the onion rings in batches—do not overcrowd the pot—for 2 to 3 minutes per batch, or until golden brown and crisp. Use a slotted spoon or spider to turn rings if needed and to remove them from the oil.
Drain fried rings on a wire rack set over a baking sheet or on paper towels. While still hot, evenly sprinkle the 1/4 teaspoon salt over the rings.
Serve immediately.