1. Preheat a gas grill to medium. Combine ground turkey, salt and mustard in a large bowl and mix with hands to blend. Divide into 4 portions and shape into patties. Make a well in each patty and fill each one with about 2 Tbsp. cheese. Form burgers around cheese, enclosing it completely. Flatten each burger slightly.
2. Oil grill grates. Place burgers on grill, cover and cook until well marked and interiors register 160ºF on an instant-read thermometer, 7 to 8 minutes per side. Transfer to buns and top with tomato, avocado and lettuce.