Season the chicken breasts with salt and pepper on both sides.
Heat 1 tablespoon of olive oil in a large skillet over medium heat.
Add the chicken breasts to the skillet and cook for about 6-7 minutes on each side, or until the chicken is fully cooked and no longer pink in the center. The internal temperature should reach 165°F (75°C).
Remove the chicken from the pan and let it rest for a few minutes before slicing it into strips.
Prepare the Salad:
In a large mixing bowl, combine the chopped lettuce and purple arugula.
Add the croutons to the salad.
Add the sliced cooked chicken on top of the salad.
Make the Honey Mustard Dressing:
In a small bowl, whisk together the Dijon mustard, honey with lemon juice, olive oil, apple cider vinegar, salt, and pepper until smooth and well combined.
Taste and adjust seasoning if necessary.
Assemble the Salad:
Divide the salad in 4 servings.
Drizzle the honey mustard dressing over the salad just before serving.