The previous night, place your chicken breasts to brine in a solution made of 1 tablespoon of salt for 2 cups of water. While this step is not absolutely mandatory, it creates a much juicier and tastier chicken and requires very little effort on your part. Trust me, it's totally worth it.
Preheat oven to 375°F
In a bowl, add all the ingredients for the cheese filling and mix delicately with a spoon until well combined. Set aside.
With a sharp boning knife, make an incision in each of the chicken breasts. Start at the larger, thicker end and slowly work your way to the pointy end, being careful not to let the blade go all the way through. You want to create a nice pocket for your cheese filling.
Insert a finger or two in that pocket to stretch it a little bit and make sure that the passage is unobstructed and goes all the way to the end.
Place the cheese filling in a large pastry bag equipped with a large round tip and pipe it into the chicken breasts' cavities. If you need to, pinch the openings between your fingers and give the breasts a gentle squeeze to evenly distribute the filling within the pocket. Set aside.
With the help of a spiralizer, cut the sweet potatoes into long strings. Use the longest strings to wrap around the chicken breasts as best you can. Note that you will have to leave quite a few strands behind as they will not be long enough to wrap around the chicken; You can keep those smaller pieces for another use.*
Place a cooling rack into a 13" x 18" baking sheet and place the now stuffed and wrapped chicken breasts onto that cooling rack. Brush the chicken breasts with the melted ghee and then sprinkle them with the chopped thyme, salt and pepper.
Bake uncovered in a 375°F oven for 20 minutes, and then lower the oven temperature to 350°F. Tent your chicken loosely with aluminium foil and resume cooking for an additional 25 minutes. Remove the chicken from the oven and let it rest for 5 minutes before serving.
If you feel the sweet potatoes could use a little more coloring after the chicken is done cooking, set the oven to broil for 2 to 3 minutes.
*Make sure that you select sweet potatoes that are as evenly shaped as possible, with a nice, elongated oval shape. This will ensure that you get the longest possible strings.