In a large bowl, gently combine the lean ground beef, ground pork, beaten egg, bread crumbs, parsley, oregano, grated Parmesan, salt, and pepper. Mix until just combined.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Brown the meatballs in batches for about 2-3 minutes per batch until lightly browned.
In a large pot, heat the remaining tablespoon of olive oil over medium heat. Add the diced onion, carrots, and celery and sauté until softened, about 6-8 minutes.