1. Rinse tomatoes, cut in half lengthwise, and place, cut sides up, in a 9-inch-wide pan. Sprinkle lightly with salt, pepper, and sugar. Finely chop enough of the mint leaves to make 2 tablespoons; mix with 1/2 tablespoon olive oil. Pat mixture onto cut sides of tomatoes. Drizzle evenly with remaining 1/2 tablespoon oil. Bake in a 400° regular or convection oven until browned on top, about 1 hour. (If pan juices begin to blacken, add a few tablespoons water to pan.)
2. Meanwhile, measure 2 cups broth. In a blender or food processor, whirl peas, remaining mint leaves, and as much of the broth as needed to process until very smooth. Pour into a 2- to 3-quart pan and add remainder of the 2 cups broth.
3. Rinse and drain scallops; pat dry. Sprinkle lightly with salt and pepper. Set a 10- to 12-inch nonstick frying pan over medium-high heat and add butter; when it's just beginning to turn brown, lay scallops, flat side down, in pan. Cook until well browned, about 2 minutes; turn to brown other sides well, and cook until scallops are opaque but still moist-looking in center (cut to test), 2 to 3 minutes longer. Meanwhile, bring pea-mint broth to a simmer over high heat, about 4 minutes. Transfer scallops equally to wide, shallow soup bowls.
4. Add remaining 1/4 cup broth and the wine to frying pan; turn heat to high and stir often to free browned bits until reduced to about 1/3 cup, 2 to 4 minutes.
5. Set 2 tomato halves on scallops in each bowl, pour hot pea-mint broth equally around scallops. Drizzle wine sauce over tomatoes, and garnish bowls with mint sprigs.