In a medium bowl, gently combine the turkey, mustard, thyme, and scallions.
Form the meat into four ¾-inch-thick patties. Season with ½ teaspoon salt and ¼ teaspoon pepper.
Heat the oil in a large nonstick skillet over medium heat. Cook the patties until cooked through, 6 to 8 minutes per side.
Meanwhile, in a bowl, whisk together the mayonnaise, vinegar, and ¼ teaspoon each salt and pepper. Toss with the lettuce and carrot.
Serve the burgers on the rolls, topped with the slaw. Serve with chips and pickles (if desired).