For the meatballs, preheat the oven to 400F and prepare a baking sheet with a baking rack inside for cooking.
Add the ham, egg, breadcrumbs, and spices to a food processor. Blend together to form a paste, the ham should be ground similar to the chicken.
Add the ham mixture to a large bowl with the chicken and cheese. Mix with your hands to distribute the ham into the chicken, then form into 35-40 meatballs, about 1 1/2 inches in diameter. Place the meatballs on the baking rack inside the baking sheet.
Bake the meatballs for 22-25 minutes at 400F.
While the meatballs are baking, combine the ingredients for the mustard sauce in a bowl. Taste, and add more salt or mustard to your preference.
Remove the meatballs from the oven and let cool for a minute or two, then serve with the sauce for dipping.
These can be made in advance, baked, then kept in the fridge for a few days. Bake again at 300F until the cheese is gooey, and serve with the dipping sauce.