How to Make It
In a food processor, pulse the bread, scallions, basil and 1 tablespoon of the olive oil until the bread is coarsely chopped.
Transfer the mixture to a large bowl. Add the ground chuck, grated cheese, 1 teaspoon of salt, 1/2 teaspoon of pepper and the remaining 2 tablespoons of oil and blend well. Shape the meat into four thick, 5-inch-long ovals. Make an indentation in the center of each meat loaf and tuck in a piece of mozzarella, then cover the cheese with the meat mixture to enclose it. Reshape the meat into ovals with slightly tapered ends.
Light a grill. Rub the meat loaves with olive oil and grill over high heat, turning, until well browned all over and firm to the touch, about 8 minutes total; the loaves should still be slightly pink in the center.
Rub the cut sides of the tomatoes with olive oil and season with salt and pepper. Grill the tomatoes, cut side down, until lightly charred, about 1 minute. Turn and grill until the tomato juices begin bubbling, about 1 minute longer. Serve the meat loaves right away, with the tomatoes.