Combine butter, parsley, and 2 teaspoons garlic in a bowl. Season with salt and pepper. Place panko on a shallow plate or bowl. Season with salt and pepper.
Combine chicken, onion, egg, plain breadcrumbs, and remaining garlic in a second bowl. Season with salt and pepper. Use about 2 ounces chicken mixture to form a meatball around 1 ounce butter mixture. Roll in panko and place on a small sheet pan. Repeat with remaining chicken mixture, butter mixture, and panko.
Heat ½ inch oil to 350ºF in a large cast-iron skillet or Dutch oven. Using a slotted spoon, lower meatballs into oil and fry, turning often, until golden brown and cooked through, 5 to 6 minutes. Serve immediately with mashed potatoes and broccolini alongside.
