Preheat the oven to 400 degrees F.
Brine the chicken as you prepare the ingredients. Instructions on brining are in the body of the blog post!
In a mixing bowl, combine the arugula, basil and 3 tbsp of goat cheese until a cheesy paste is formed. The greens should be comfortably coated in the cheese. Set that cheese mixture aside along with the extra 1 tbsp of goat cheese that you reserved.
Heat an oven-safe skillet over medium heat. Season with about 1 tbsp of olive oil. Add the sliced peaches to the skillet and sauté for 5 minutes, until slightly soft and golden brown. Then, add 1/3 cup of balsamic vinegar and lower the heat. Continue to sauté until the balsamic vinegar reduces and becomes a thick syrup. If it doesn't seem to be thickening, turn up the heat and bring the vinegar to a boil. It should thicken very quickly. Once the balsamic vinegar is syrup-y, remove the peach mixture from the heat and save any extra balsamic reduction in a separate bowl.
Remove the chicken from the brining liquid and place the breasts onto a paper towel. Thoroughly dry off the chicken on all sides.
Carefully take a large knife and slice the chicken breast lengthwise, in the middle of the breast. Don't slice all the way through. Stop when you're about 3/4 the way through the chicken breast. It should open up like a book. Repeat with the second chicken breast.
Take the peach mixture and set aside 2 tbsp of peaches for your salad. Place the rest of the peaches into a new bowl. You'll be using your hands to stuff these into the chicken, so it's important you don't include the salad peaches in the same bowl!
Open up each chicken breast and generously spread a layer of the goat cheese and greens mixture onto the surface. Next, add a layer of the sliced peaches. Top the peaches with a little more of the goat cheese and greens mixture, then add some small dollops of plain goat cheese on top and around the sides of the peaches. The goal here is to create layers of creamy, crunch, tangy, earthy and tart flavors! Layer however you would like, or watch the video to see how I did it!
Once the chicken breasts are stuffed, dry them off one more time and sprinkle salt on the top and bottom. Feel free to also season them with pepper.
Use the same oven safe skillet that you made the balsamic peaches in to cook the chicken. Heat the skillet over medium high heat and season it with olive oil. Once the oil is shimmering, place the chicken breast onto the pan and let it sear for 4-5 minutes, until slightly golden brown on one side. Flip and repeat with the other side. Then, pop the entire skillet into the oven for 10-20 minutes, until the chicken is fully cooked. Every chicken breast is different, so just check on yours after 10 minutes to be safe!
While the chicken is in the oven, make the salad (if serving with salad.) In a small bowl or mason jar, mix together the olive oil, balsamic vinegar and salt to create a simple vinaigrette. Taste the vinaigrette to make sure that the salt and acid levels are to your liking.
5 minutes before the chicken is ready, pour the dressing over the arugula and toss. Plate about 1 cup of salad for each person and top with the leftover balsamic peaches.
OPTIONAL: If you want to make more balsamic reduction to drizzle on top, heat 1/2 cup of balsamic vinegar over medium high heat and bring it to a boil. Lower the heat to medium low and let it cook until the consistency is thicker and sticks to the spoon.
Remove the chicken from the oven and slice with a sharp knife. Serve with the salad and enjoy immediately!