Toss the shishito peppers, cherry tomatoes and 1 tablespoon vegetable oil in a large bowl.
Heat the remaining 1 tablespoon vegetable oil in a large skillet until hot but not smoking. Add the tomato-pepper mixture and stir-fry until blistered in spots, 3 to 4 minutes. Remove from the heat; stir in the scallions, ginger and 1/2 teaspoon salt.