Mix all the chicken rub ingredients together in a small bowl.
Rub the spices onto the entire chicken breast. Slice a pocket into the chicken on the thickest side of the chicken, about 3 inches wide and 3/4 of the way through the chicken breast. Be careful not to slice all the way through the chicken.
Heat 1 tablespoon of oil in a cast iron skillet over medium-high heat. Once hot, add the chicken and sear 2-3 minutes or until both sides are golden-brown. Remove from the skillet and set aside.
Add the remaining 1 tablespoon oil into the skillet and reduce heat to medium-low heat. Add sliced mushrooms and saute 3-4 minutes. Stir in thyme, oregano, salt, and pepper. Add garlic cloves and saute for 1-2 more minutes. Remove from heat and stir in goat cheese.
Carefully place the mushroom and goat cheese mixture into each of the pockets cut into the chicken breast. Place as much as you can into each pocket. It is ok if some is spilling out a little bit of the chicken breast.
Place the stuffed chicken breast back into the cast iron skillet. Bake for 25-30 minutes or until the thickest part of the chicken reaches 165 degrees F.
Remove from the oven and let rest a few minutes before serving. Enjoy!