In a large mixing bowl, combine ground chicken, breadcrumbs, grated parmesan, egg, salt, pepper, finely chopped onion, and minced garlic. Mix until fully incorporated; the mixture should feel slightly sticky. Form the mixture into uniform meatballs, about 1.5 inches in diameter, and set them aside on a plate while you prepare to brown them.

Heat 2 tablespoons of olive oil in a large skillet over medium heat. Once hot, carefully add the meatballs, ensuring they do not touch each other to achieve even browning. Cook for about 4-5 minutes on each side until they are golden brown all over. Once browned, transfer the meatballs to a plate and cover to keep warm.

In the same skillet, add another tablespoon of olive oil if needed, then toss in the diced onion, carrot, and celery. Sauté over medium heat for about 5-7 minutes until they soften, stirring frequently. Add one tablespoon of tomato paste and cook for an additional minute.

Pour in the red wine and chicken broth, scraping up any browned bits from the skillet's bottom. Bring the mixture to a gentle simmer, allowing it to reduce for 15-20 minutes.

Once the sauce has reduced, gently return the browned meatballs to the skillet. Cover the pan and let the meatballs simmer in the sauce for an additional 20-30 minutes over low heat, stirring occasionally.

Prepare the cheesy polenta by bringing 4 cups of water or chicken broth to a boil in a separate saucepan. Gradually whisk in 1 cup of polenta and reduce the heat to low. Stir frequently and cook for 10-15 minutes until thickened and creamy. Once done, mix in the remaining parmesan cheese, butter, and adjust salt to taste.

To serve the Red Wine Braised Meatballs, spoon a generous portion of creamy cheesy polenta onto each plate. Top with the succulent meatballs and drizzle the rich sauce over them. Optionally, garnish with freshly chopped parsley.