Preheat the oven to 375 degrees F.
Use a sharp knife to carefully cut a pocket into the sides of each of the chicken breasts, being careful not to cut all the way through.
Sprinkle the salt on the inside and outside of the chicken breasts.
In a medium bowl, add the cream cheese, the garlic, the pesto, and the mozzarella cheese and stir to combine.
Stuff the cream cheese mixture, the sun-dried tomatoes, and the spinach inside the pockets of the chicken breasts, then secure the pockets with a toothpick if needed.
In a large cast-iron skillet or oven-safe skillet over medium heat, add the olive oil.
Add the stuffed chicken breasts to the olive oil and sear on both sides until golden-brown, about 3-4 minutes.
Bake until the chicken breasts are cooked through and reach an internal temperature of 165 degrees F, about 16-18 minutes.
Serve the stuffed chicken breasts garnished with the parsley.