Heat oven to 400ºF.
Chill the chicken in the freezer for 15 minutes.
Meanwhile, place the Parmesan chunks in the food processor and pulse 15 times. Add the bread pieces and pulse 5 times. Reserve 1 cup of the breadcrumb/cheese mixture, then add the parsley, basil, oregano, and black pepper to the food processor bowl and pulse 5 times. Transfer the herbed breadcrumb mixture to a large bowl.
Remove the chicken from the freezer and pulse it 8 times in the food processor until it resembles a medium grind.
Add the chicken, egg, garlic powder, and salt to the bowl with the herbed breadcrumb mixture. Using your hands, gently combine until just incorporated, trying not to overwork the meat.
Divide the meatball mixture into 32 golf ball-size rounds (1-ounce each) and roll them in the reserved breadcrumb mixture.
Heat 2 tablespoons of the olilve oil in a 10-inch oven-safe skillet over medium heat. Brown the meatballs in the oil in two batches. Brown the first batch for 2 to 3 minutes per side for a total of 4 to 6 minutes total browning time. Brown the second batch for 2 minutes longer. Remove the browned meatballs from the pan to a plate and deglaze the pan with the wine, scraping up any bits on the bottom of the pan with a wooden spoon.
Add the reserved tomato liquid and the prepared sauce, then return all of the meatballs to the pan, placing the meatballs that cooked slightly longer toward center of the pan and the short-cooked ones nearer to the edge (this way they’ll finish cooking at the same time and you won’t end up with overdone meatballs in the outside ring). Combine the grated mozzarella and fontina in a small bowl and sprinkle the mixture over top the meatballs.
Bake until the meatballs are cooked through and the cheese is melted, about 10 minutes. Serve over cooked pasta, on top of crispy bread, or inside a hoagie roll.