Heat the olive oil in a Dutch oven over medium heat. Add in the sirloin, pork and veal, and brown until no longer pink, about 10 minutes. With a slotted spoon, remove the meat and store in a bowl, leaving the juices and fat in the Dutch oven.
Sweat the garlic, onions and Italian seasoning in the Dutch oven, stirring frequently to insure they do not burn. Once the onions are translucent, add the meat back to the pan and then add the wine to deglaze. Add in the tomatoes and milk and bring to a simmer, stirring frequently until the sauce thickens, about 15 minutes. Season with salt and pepper.
Sandwich Build: Place a piece of cheese in each hoagie roll. Place some meat on top and the some giardiniera on the top of it all. Serve with a pint of Chianti.