Pre-heat the oven to 325°F.
Combine the sauce ingredients in a food processor and puree to smooth. Place in a saucepot and gently simmer over low heat for 30 minutes to thicken and combine the flavors.
Soak the bread in the milk.
Place the meats in a bowl and add the seasonings, garlic, parsley, eggs, cheeses and EVOO, two turns of the bowl. Squeeze the excess liquid from the bread and crumble as you add it to meat. Combine the meatball mixture and form six patties. Arrange on a baking sheet and roast for 20-25 minutes to cook through.
Switch on the broiler when you remove the burgers from the oven. Place a rack at the center of the oven.
Arrange the toasted bun bottoms on a baking sheet. Turn the burgers in the sauce and set them on the bun bottoms. Top with the sliced mozzarella or provolone and melt to bubbly under the broiler. Top with torn basil and any remaining sauce and set the bun tops in place.