Preheat oven to 350°. In a small bowl, gently toss tomatoes with about 1/8 tsp. each salt and pepper; set aside.
Toast nuts in a shallow pan in oven until golden, 5 to 8 minutes; let cool. Meanwhile, fill a medium pot halfway with water and bring to a boil. Fill a bowl with ice and water. Stir basil and parsley into boiling water and cook just until leaves wilt, 10 to 15 seconds. Immediately drain leaves, add to ice water, and let cool. Drain herbs, roll in a kitchen towel, and press out water.
In a food processor, pulse garlic and walnuts until finely chopped. Add herbs, 1/2 tsp. salt, 1/4 tsp. pepper, and the oil; pulse pesto until puréed.
Split rolls and set cut-side up on a rimmed baking sheet. Generously spread roll bottoms with pesto. Arrange mozzarella and tomatoes on pesto and season with more salt and pepper to taste. Cover with bread tops.
Bake sandwiches until cheese and tomatoes soften and bread is crusty, 10 to 14 minutes; drape with foil if they cook beyond 10 minutes.