Preheat the oven to 400°F and cook the rice according to package instructions.
Cut the tops off the tomatoes and scoop out the centers with a spoon or melon baller, leaving enough flesh so the walls remain sturdy. Set the tomatoes upside down to drain.
Heat 1 tablespoon olive oil in a skillet over medium-low heat. Add diced onions, garlic, and ground elk. Sauté until the meat is browned, then remove from heat.
In a large bowl, combine the cooked meat mixture, rice, diced green chiles, tomato paste, 1¼ cup shredded cheese, chili powder, cumin, granulated garlic, and salt. Mix well.
Fill each tomato with the mixture and place them in a baking dish. Drizzle with remaining olive oil and top each tomato with Parmesan and the remaining shredded cheese
Bake for 25–30 minutes, until the filling is heated through and the cheese is melted.
Serve warm with salsa, sour cream, guacamole, and a sprinkle of fresh cilantro.