Preheat the oven to 400 degrees F or 200 degrees C.
Combine salt, pepper and Italian herbs in a small bowl and set aside.
Cut a lengthwise slit in the chicken with a sharp knife to create a pocket. Do not cut all the way through.
Coat the inside and the outside of the chicken with the seasoning mix.
Heat olive oil in a large oven-safe skillet over medium heat.
Sear the chicken for 3-4 minutes or until a nice crust forms, then flip it over and repeat the process. You may need to cook two at a time, depending on how large your skillet is.
Remove the chicken from the pan and set it aside on a plate.
Add the asparagus, lemon juice, and balsamic vinegar to the pan. Cook for 30 seconds or until the liquid starts to bubble up.
Using a slotted spoon, remove the asparagus from the pan and set aside, leaving the cooking liquid in the pan.
Gently open the pocket of each chicken breast and add 2 slices of the cheese and 3-5 spears of asparagus to the center, then top with another slice of cheese.
Close the pocket with 5-6 toothpicks, return the chicken to the skillet, and place in the preheated oven.
Bake for 15-20 minutes or until an instant thermometer reads 165 degrees F or 74 degrees C when inserted into the thickest part of the chicken.
Let the chicken rest for at least 10 minutes before removing the toothpicks. Garnish with freshly chopped basil or parsley and lemon slices, if desired.