Light a grill for medium-high heat.
Toss the scallops with the pesto and let stand at room temperature as the grill heats up, about 20 minutes.
Melt 3 tablespoons of the butter in a medium skillet over medium heat. Cook until the butter turns a nutty brown color, 3 to 5 minutes, swirling the pan now and then. Remove from the heat and stir in the lemon juice, scallion, salt, and pepper. Brush the butter mixture generously over the inside of the tomatoes.
Put bread in food processor and process to crumbs. Add the remaining 2 tablespoons of the butter to the skillet over medium heat. Stir in the bread crumbs and cook until toasted golden brown, 3 to 4 minutes, stirring now and then. Remove from the heat and stir in the cheese.
Brush the grill grate and coat with cooking spray. Grill the scallops until grill-marked and no longer translucent in the center, 3 to 4 minutes per side (about 120ºF internal temperature). Stuff a grilled scallop into each seasoned tomato. Pack the bread crumbs on top of the scallops. Grill the stuffed tomatoes directly on the grill grate with the lid down until warm, 1 to 2 minutes. Serve 2 tomatoes per person on a bed of the lettuce leaves.
Tip: Ask for “dry” or unsoaked scallops from the seafood counter. Soaked scallops are too wet to develop a crusty brown surface on the grill.