Prepare a medium-high gas or charcoal grill fire.
Tear half of one roll into 1/4-inch pieces and put in a small bowl. Add 1/4 cup water and let sit until the bread has absorbed the water, about 5 minutes. Gently squeeze the bread to remove excess water and finely chop the soaked bread (you should have about 1/4 cup).
In a large bowl, break up the pork with your hands. Add the soaked bread, egg, garlic, lemon zest, thyme, smoked paprika, 1-1/4 tsp. salt, and 1/2 tsp. pepper. Use your hands to gently combine the mixture. Shape into 16 meatballs (each about 1-1/2 inches).
Split the remaining rolls, but don’t cut them completely in half. Brush the insides of the rolls with 1 Tbs. of the olive oil. Brush the cut side of the tomato and the meatballs with the remaining olive oil.
Oil the grill grate and grill the tomato until softened and lightly browned, turning once, 4 to 6 minutes. Grill the bread split side down until golden and lightly charred on the edges, 1 to 3 minutes. Grill the meatballs until they’re just cooked through, turning once, about 8 minutes. Remove each item as it finishes cooking and set aside.
In a food processor, purée the grilled tomato, piquillo peppers, and red pepper flakes. Season to taste with salt.
Put 4 meatballs in each roll and top with one-quarter of the sauce and one-quarter of the cheese. Serve hot.