Heat canola oil in the skillet until cooking thermometer reads 350F. While shaping the meatballs, be sure to check the oil temperature often. If the oil is heating too quickly, turn the heat down slightly.
In a medium bowl, combine ground chicken, ½ teaspoon ground black pepper, 1 egg and ½ cup regular breadcrumbs. Mix gently until mixture is well incorporated. Using a 1½” scoop (or tablespoon), form meatballs into 1½” balls, flatten each meatball slightly and place slice of ham and a slice of cheese (stacked) in the middle of each ball. Bring the sides of each meatball up and over the ham and cheese, then “pinch” the meat back together. Slightly roll each meatball to reshape into meatballs.
*Be sure to keep checking the oil temperature.
In a small bowl, combine regular breadcrumbs, panko breadcrumbs, pepper and grated Parmesan. In a different small bowl, combine the beaten eggs and water and mix until combined.
Set the bread crumb bowl and the egg/water bowl on the counter next to the skillet with the hot oil. Place a paper towel-lined plate nearby.
Once the oil has reached the desired heat, dip a meatball in the egg mixture and then roll it in the breadcrumb mixture. Carefully, place the meatball in the hot oil and repeat until half the meatballs are in the oil. Cook, turning gently to cook all sides, until meatballs are cooked through. Be careful not to burn the meatballs. When cooked through, transfer meatballs to paper towel-lined plate. Repeat process with the other half of the meatballs.
After cooking the meatballs, pour the used oil (very carefully) into a heatproof container and set it aside until cool enough to discard.
Place prepared sauce in the skillet over low heat. Once sauce has reheated, place meatballs over sauce and serve.
**Make ahead. The sauce and meatballs can be prepared (separately) and kept refrigerated up to two days before serving. When ready to serve, place sauce in skillet and place meatballs over the sauce. Cook over low until heated through.