Bring the frying oil to 350°F (180°C) in a pot over medium heat. Use an oil thermometer to check the temperature rather than judging it by surface movement.
Work the salt, pepper, and onion powder evenly through the ground beef in a bowl. The finished mixture should have seasoning distributed throughout, without large pockets of spice.
Remove the onion skin, cut ½-inch (1-centimeter) slices, and gently separate the layers into individual rings. Choose small to medium rings that can hold the cheddar without requiring a thick mound of beef.
Spread a spoonful of seasoned beef across the bottom opening of an onion ring. Press it against the inside edge so the onion supports a continuous layer of filling.
Nestle a cheddar square into the middle, then cover it with another spoonful of beef. Flatten the top and join the beef layers firmly around the cheese, leaving no exposed edges or openings into the pocket.
Fill the remaining suitable rings using the same beef-cheese-beef arrangement. Keep their surfaces level with the onion edges so the filling has a consistent thickness.
Arrange separate bowls of flour, beaten eggs, and panko in that order. Keep the coatings apart so the flour stays loose and the crumbs remain easy to press onto the rings.
Dust each stuffed ring with flour, tap away the excess, and coat it with egg, panko, egg again, and a final layer of panko. The finished coating should cover both faces and the outer onion edge without bare patches.
Lower the coated rings carefully into the oil and fry for 5–6 minutes, maintaining the frying temperature. Look for a deep golden-brown crust and verify that the thickest beef portion reaches 160°F before serving.
Lift the cooked rings onto paper towels to absorb surface oil, then serve with ketchup. The crust should feel crisp, with melted cheddar enclosed inside the cooked beef.