Preheat oven to 325F.
Combine sauce ingredients in a food processor and pure to smooth. Place in a saucepot and gently simmer over low heat for 30 minutes to thicken and combine flavors.
For the burgers, soak bread in milk.
Place meats in a bowl and add seasonings, garlic, parsley, eggs, cheeses and olive oil, 2 turns of the bowl. Squeeze excess liquid from bread and crumble as you add it to meat.
Combine meatball mixture and form 6 patties. Arrange on a baking sheet and roast 20-25 minutes to cook through.
Switch on broiler when you remove burgers from oven. Place rack at center of oven.
Arrange toasted bun bottoms on a baking sheet. Turn burgers in sauce and set on bun bottoms. Top with sliced mozzarella or provolone and melt to bubbly under broiler. Top with torn basil and any remaining sauce and set bun tops in place.