Heat oil in a pot over medium heat to 350°F (180°C). Place the flour, eggs, and bread crumbs into three separate bowls.
In a bowl, mix together the ground beef, salt, pepper, and onion powder. Peel and slice the onion into 1-centimeter (½ inch) rings. Detach the rings from each other.
Take a spoonful of the beef mixture and press it into the bottom of a ring. Push a cheddar square into the center of the beef. Seal the top with another spoonful of the beef, pressing it flat. Repeat with the rest of the rings.
Dip a ring into the flour, shaking off excess, then into the egg, the bread crumbs, then back to the eggs, and one last time into the breadcrumbs. Repeat with the remaining rings.
Deep-Fry
Fry the rings for 5–6 minutes, until deep golden-brown.
Drain on a paper towel, then serve with ketchup or ranch!