Soak the bread in milk and squeeze dry.
Heat 1 tablespoon of oil in a large shallow earthenware casserole dish or Dutch oven over medium heat.
Add ½ cup of onion and the ham, cook until onion is wilted and transparent (about 5 minutes).
Transfer to a large bowl.
Wipe out the casserole dish and add another 1 tablespoon of oil.
Cook bell peppers, garlic, and remaining ¼ cup onion until peppers are softened (about 8 minutes).
Transfer to a medium bowl and reserve.
In the bowl with onion-ham mixture, add veal, pork, egg, salt, pepper, bread, and 1 tablespoon parsley.
Mix well.
Shape the mixture around each cheese cube to form 1¼-inch balls.
Lightly dredge in flour.
Heat the remaining 1 tablespoon oil in the casserole dish over medium heat.
Add meatballs and cook until browned on all sides.
Return the pepper mixture to the casserole dish, stir in paprika, thyme, wine, and broth.
Season with salt and pepper.
Bring to a boil, then reduce heat to low, cover, and simmer for 45 minutes.
Transfer the meatballs to a warm platter.
Pass the sauce through a strainer into a small bowl.
For optional tempura vegetables: In a medium bowl, mix water and salt.
Soak eggplant for 30 minutes, drain, and let dry on paper towels.
Prepare batter according to Batter-Fried Squid Tentacles instructions.
Heat oil in a skillet or deep fryer.
Dip each vegetable in batter and fry until golden.
Drain on paper towels.
Pour the sauce onto a platter or individual dishes, place the meatballs in the sauce.
If using tempura vegetables, arrange them over the dish, sprinkle with parsley, and serve hot.