In a large bowl, combine the ground meats, breadcrumbs, Parmesan cheese, egg, salt and pepper with your hands, mixing just until blended but not overworking it, which could result in tough meatballs.
Shape small handfuls (as much as you’d use for a small burger) of the mixture around each wedge of cheese, pressing to seal any gaps and make smooth meatballs about the size of a small orange. Preheat the oven to 350°F.
In a large, heavy, preferably ovenproof skillet, heat a drizzle of oil over medium-high heat. Add the meatballs in batches and brown, rolling them around as you need to until they are golden and crispy on all sides. Transfer them to a plate while you finish browning all the meatballs, then return them all to the pan or transfer to a 9”x13” baking dish and bake for 20-30 minutes, just until cooked through. Serve on spaghetti or in soft rolls, with warmed tomato sauce.
Serving Size Makes 8-12 giant meatballs.