Heat oven to 450.
Slice onions crosswise into 1/2 inch thicknesses. Separate into rings. Select 8 of the largest rings. Reserve remaining onions for another use. Cut cheese into 8 small dice.
Combine beef, onion powder, salt, and pepper in a small bowl. Place flour in another bowl, panko in another bowl, and eggs in a fourth bowl. Beat eggs until frothy.
Heat oil in a medium saucepan over medium heat.
While oil is heating, place 2 tablespoons beef mixture inside one onion ring. Smash it down until it fills the bottom half of the ring. Top with one cheese cube. Smash another tablespoon of beef mixture on top of the cheese, filling the onion ring. Repeat with remaining beef, cheese, and onions.
Working with one stuffed onion ring at a time, dredge onion ring in flour, then dip in egg, then dredge in panko. Repeat: flour, then egg, then panko for a second layer of each. Place in pan with hot oil. Cook 1 minute per side. Remove to a parchment-lined baking sheet. Repeat with remaining stuffed onion rings.
Bake at 450 for 10 minutes, then flip and cook an additional 10 minutes. Serve with 9010-approved ketchup, if desired.