1. Combine zucchini, garlic, basil, Parmesan, lemon juice, and 1 tablespoon oil in a food processor; process until smooth. Transfer to a small bowl.
2. Preheat a lightly oiled grill over medium-high heat. Season chicken with salt and pepper; grill until golden and cooked through (about 4-5 minutes). Transfer to a cutting board; slice in half. Toast cut sides of rolls on grill until golden on one side (about 1 minute).
3. Top bottoms of rolls with half of chicken and pesto; top with middle piece of roll. Layer rolls with remaining half of ingredients and tomato slices. Top with remaining part of roll. Serve.