For the shrimp: Mix the soy sauce, brown sugar, ginger and garlic in a large resealable plastic bag. Add the shrimp to the bag and seal. Let marinate at least 5 minutes and up to 15 minutes. For the dressing: Whisk the olive oil, lime juice, brown sugar, ginger and jalapeño in a small bowl. Preheat the broiler. Remove the shrimp from the marinade, transfer to a rimmed baking sheet or broiler pan and broil until opaque, pink and slightly charred, about 4 minutes. Transfer the shrimp to a plate and let cool slightly, saving any juices on the baking sheet. For the salad: In a large bowl, toss the salad greens and tomatoes with about three-quarters of the dressing. Arrange the shrimp on top and drizzle with the remaining dressing and any juices from the baking sheet.