Prepare a grill for indirect heat. If using a charcoal grill, build hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
For the meatballs: Combine the ground chicken, ricotta, Parmesan, breadcrumbs, parsley, nutmeg, garlic, egg and onion in a medium bowl until just mixed. Do not overwork. Season with salt and pepper. Divide the mixture into 8 portions and roll into balls.
Heat a cast-iron pan on the hot side of the grill until nice and hot. Brush the pan with enough olive oil to liberally coat the surface, about 3 tablespoons.
Place the meatballs in the pan and cook, flipping them, until all sides are caramelized, about 3 minutes. Move the pan to the indirect-heat side of the grill and cover the grill. Cook for 5 minutes.
For the sauce: Add the garlic, oregano and onion to the pan with the meatballs and saute until the onions begin to soften, 2 to 3 minutes. Flip the meatballs, then add the tomato puree and 1/2 cup water. Season with salt and pepper. Cover the grill and continue to cook until the chicken is cooked through and the sauce is reduced slightly, 10 to 15 minutes.
For topping and serving: Top the meatballs with the mozzarella, cover the grill and cook until the cheese is melted, about 3 minutes. Discard the oregano sprig. Spoon the meatballs on top of the Soft Polenta. Spoon any remaining sauce over top and serve topped with the Parmesan and basil if using.
(Alternatively, you can cook the meatballs and the sauce as directed in a cast-iron skillet on the stovetop over medium heat, then transfer the skillet to a 400 degrees F oven for 10 to 15 minutes before melting the cheese.)
Add 4 1/2 cups water, 1 tablespoon salt and the olive oil to a medium saucepot and bring to a simmer over medium heat. Whisk in the cornmeal in a steady stream, until it is all incorporated and smooth. Reduce the heat to medium low and continue to cook at a simmer until the polenta is creamy and fully hydrated, 30 to 40 minutes. Take the saucepot off the heat and whisk in the butter and Parmesan. Season with additional salt and pepper. Transfer the polenta to a large serving bowl.