Transfer the mixture to a large bowl. Add the ground chuck, parmesan, 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, tuck in the mozzarella, then cover the cheese with the meat mixture to enclose it. Reshape the meat into ovals with slightly tapered ends.
Heat your grill and rub the meat loaves with olive oil. Grill on high heat, turning until well browned and firm to the touch, about 8 minutes total.
The uncooked meat loaves can be refrigerated overnight and brought to room temperature before grilling for an even easier meal!