In a small bowl, combine soy sauce, vinegar and 1/4 teaspoon of the sesame oil and mix well. In another small bowl, stir mayonnaise with the remaining 1 1/4 teaspoons sesame oil; set aside.
Place flour and egg in 2 separate bowls. Season fish slices with salt and pepper. Dredge fish in flour, dusting off excess, then place on a large plate.
In a large nonstick skillet, heat safflower oil over medium. Dip each piece of breaded fish one at a time in beaten egg, then place in skillet. Cook until golden and cooked through, 2 to 3 minutes per side. Transfer to a paper towel-lined plate to drain and season with salt.
Add scallions and lettuce to soy sauce dressing, season with salt and pepper and toss to evenly coat. Smear cut sides of rolls with some of the sesame mayonnaise. Divide scallion salad on bottom buns and top each with 1 jeon. Arrange pickles on top and close sandwiches; serve immediately.