Start by peeling the onions and slicing them into thick rings, about 1/4 to 1/2 inch thick. Carefully separate the rings and set them aside.
In a large mixing bowl, combine the all-purpose flour, baking powder, paprika, garlic powder, and a pinch of salt. Whisk the dry ingredients together until well mixed.
In another bowl, crack the three large eggs and whisk them until well beaten. This will help the breadcrumbs adhere to the onion rings.
In a separate bowl, mix the panko breadcrumbs with the grated parmesan cheese. This will give your onion rings that crispy, cheesy coating.
Take each onion ring and first dip it into the flour mixture, ensuring it's well coated. Shake off any excess flour before dipping it into the egg wash. Finally, coat the onion ring with the panko and parmesan mixture, pressing gently to help the crumbs stick. Repeat this process for all the onion rings.
For frying, heat your oil in a frying pan over medium heat. Once the oil is hot, carefully place the onion rings in the oil, cooking them in batches to avoid overcrowding. Fry until golden brown, about 2-3 minutes per side. Remove and place on a cooling rack to drain excess oil.
For baking, preheat your oven to 425°F (220°C). Line a baking sheet with parchment paper and arrange the coated onion rings in a single layer. Bake for about 20-25 minutes, flipping halfway through, until they are crispy and golden brown.