Preheat oven to 400°F. Heat 1 tablespoon oil in a medium skillet over medium-low. Add onion, mushrooms, and garlic; cook, stirring often, until onion is softened, 5 to 6 minutes. Remove from heat; let cool 5 minutes.
Stir together panko, Parmesan, Pecorino Romano, parsley, rosemary, mint, salt, and pepper in a large bowl until combined. Stir in pork, egg, and cooled onion mixture until thoroughly combined. Slowly add ¼ cup water, stirring until incorporated. Cover mixture, and refrigerate at least 1 hour or up to 24 hours.
Line a large rimmed baking sheet with aluminum foil; coat with remaining 2 teaspoons oil. Shape pork mixture into 28 (1-ounce) meatballs; transfer to baking sheet. Bake in preheated oven until an instant-read thermometer inserted in center of meatball registers 160°F, 15 to 17 minutes.
Serve meatballs over polenta; drizzle with additional olive oil. Sprinkle with Parmesan and parsley; serve hot.
