Preheat oven to 425° F.
Cut a 3-inch-wide pocket in the side of each chicken breast, being careful not to slice all of the way through. Pat the chicken dry with paper towels and season with salt and pepper on all sides.
In a large bowl, stir together the cream cheese, feta, spinach, garlic, basil, oregano, onion powder and ½ teaspoon kosher salt.
Stuff the cream cheese mixture into the pocket of each chicken breast.
Heat oil and butter in a large cast iron skillet over medium heat. Add the chicken breasts to the pan and cook just until golden brown on each side, about 3-4 minutes per side. Transfer the skillet to the oven and continue cooking for about 12-15 more minutes, or until the meat reaches an internal temperature of 165° F.
Remove chicken to a cutting board and let rest for about 5 minutes before serving.
