Preheat oven to 425F.
Place the torn bread in a small bowl with the milk (make sure all the bread is submerged) and reserve.
In a large bowl, combine the ground meats, garlic, parsley, grated Parmigiano, allspice, egg, salt and freshly ground black pepper. Squeeze out the excess milk from the soaking bread (it should be loose and in small pieces) and add it to the meat mixture. Mix everything with your hands to combine.
Divide the meatball mixture in half, and score each half into eight sections with the back of your hand. Take one of the portions of the meatball mix and slightly flatten it out in your hand. Place a cherry tomato in the center and evenly wrap the meat around the tomato, completely encasing it in the meat.
Transfer the stuffed meatball to a baking sheet, using one half of the baking sheet for the tomato ones and the other for the bocconcini ones so you can keep track of which is stuffed with what. Repeat the processes until the rest of the tomatoes and bocconcini have all been rolled in a portion of the meatball mixture. Drizzle the stuffed meatballs with some EVOO, transfer to the oven and roast 15-18 minutes, until golden brown and firm to the touch.
While the meatballs are cooking, place a saucepot over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the canned tomatoes and break them up with a potato masher or the back of a wooden spoon. Add a little salt and pepper, bring up to a bubble and simmer while the meatballs are cooking.
Once the meatballs are ready, remove the sauce from the heat and stir in the pesto. If you are using store-bought pesto, add in the lemon zest. Transfer all of the sauce into a serving dish and nestle all of the meatballs into the sauce, keeping the cherry tomato-stuffed ones on one side and the bocconcini-stuffed ones on the other. Serve with some sliced crusty bread alongside.