In a bowl, combine the chicken, breadcrumbs, ¼ cup Parmesan, egg, 1 teaspoon minced garlic, 1 teaspoon Italian seasoning, and ½ teaspoon each salt and pepper.
Roll the meatballs into 1-inch balls.
In a heat-proof skillet, heat 2 tablespoons olive oil over medium heat.
Add meatballs and brown on all sides, about 10 minutes. Remove the meatballs from the skillet and set aside.
Add the remaining 2 tablespoons oil to the skillet along with the onion. Saute to soften, about 5 minutes. Add the remaining 2 teaspoons minced garlic and stir.
Add the tomato paste and stir to combine. Cook until beginning to caramelize, about 3 minutes.
Deglaze with the red wine, scraping the bottom of the pot. Bring to a simmer and cook for 2 minutes.
Add the tomatoes, crushing by hand or with a spatula while adding to the pot. Add the remaining 1 teaspoon Italian seasoning and ½ teaspoon each salt and pepper. Bring to a simmer.
Add the meatballs back to the skillet, nestling them into the sauce. Cover and cook for 10 minutes to thicken the sauce.
Top the meatballs with the remaining 1 cup Parmesan and mozzarella cheese. Transfer to the oven and cook until the cheese is melted, about 10 minutes.