Place the grated onion and tomato in a fine-mesh sieve over the sink and stir a few times, pressing on the mixture to drain the excess liquid. (Some moisture should remain; do not squeeze in a dish towel.) Transfer the remaining onion and tomato to a large bowl.
Add the beef, lamb, panko, egg, mint, parsley, garlic, oregano, coriander and cumin, plus 1½ teaspoons salt and ½ teaspoon pepper; mix gently but thoroughly.
Using a 2 tablespoon-scoop or two spoons, form meatballs that are about 1½ inches wide. Place them on a plate, cover and chill for at least 30 minutes, and up to 24 hours, to allow the meatballs to firm up.
In a large (12-inch) skillet, heat the oil over medium-high. When the oil is hot (it should sizzle immediately if you drop a bread crumb into the pan), fry the meatballs in 2 to 3 batches, flipping occasionally and lowering the heat as necessary to prevent them from getting too dark, until browned all over and just cooked through, 5 to 7 minutes.
Transfer the cooked meatballs to a paper towel-lined plate, and serve hot or warm with any combination of tzatziki, salad and pita, if desired.