Preheat a grill to high on one side; keep the other side unlit. Pull some of the bread from inside of rolls. In a food processor, grind into crumbs. Measure out 1/3 cup of crumbs.
Brush the tomatoes with some EVOO; season. Grill on the lit side of the grill, cut side down, covered and turning once, until softened, about 8 minutes. In a blender, puree the tomatoes and 1 tbsp. EVOO; season.
In a large bowl, mash the garlic, anchovies and 1/4 tsp. salt. Whisk in the egg. Mix in the onion, meats and breadcrumbs; season. Shape into 16 two-inch balls.
Brush the unlit side of the grill with EVOO. Grill meatballs, covered and turning occasionally, until barely pink in the center, 10 minutes.
Brush the cut sides of the rolls with EVOO; grill 3 minutes. Spoon some sauce on the roll bottoms, top each with 4 meatballs, sprinkle with cheese and add roll tops. Wrap in foil; place on the unlit side of the grill. Cover; cook to melt the cheese, 2 minutes.