Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the bell peppers over direct medium heat, with the lid closed as much as possible, until blackened and blistered all over, 10 to 12 minutes, turning occasionally. Place the peppers in a bowl and cover with plastic wrap to trap the steam. Let stand for about 10 minutes. Remove the peppers from the bowl and peel away and discard the charred skins. Cut off and discard the tops and seeds, coarsely chop the peppers, and transfer to a blender. Add the oil, vinegar, almonds, tomato paste, garlic, and cheese. Puree the mixture, transfer it to a bowl, and stir in the basil, salt, and pepper. Set aside.
In a medium bowl gently combine the meatball ingredients. With wet hands, form 16 meatballs of equal size. Don’t compact the meat too much or the meatballs will be tough. Gently flatten each meatball with your hand.
Grill the meatballs over direct medium heat, with the lid closed as much as possible, until they are cooked to medium doneness, about 8 minutes, turning once. During the last minute of grilling time, toast the rolls, cut side down, over direct heat. Remove the meatballs and rolls from the grill.
Place three or four meatballs (depending on the size of the roll) on the bottom half of each roll, and top the meatballs with an equal amount of dressing. Put the top of each roll in place. Serve immediately.