Cut each chicken breast diagonally across the width into 3 pieces. Whisk together mustard, tarragon, pepper and 3 tbsp (45 ml) olive oil and brush over chicken.
Place panko on a plate and season with salt. Press breasts into panko to coat on all sides.
Heat remaining 1 tbsp (15 ml) oil in a large skillet over medium heat. Working in batches, fry breasts for one minute per side or until lightly browned, adding more oil to pan as needed. Place on a baking sheet and bake for 15 minutes, turning once, or until juices run clear.