In a bowl, mix the softened cream cheese, shredded pepper jack, chopped red bell pepper, onion, garlic powder, and onion powder. Stir until everything is evenly combined and creamy. Set aside while you prep the chicken.
Using a sharp knife, carefully slice a pocket into the thick side of each chicken breast. Be careful not to cut all the way through. Leave about half an inch on each side so the filling stays inside.
Divide the cheese mixture evenly and spoon it into each chicken pocket. Gently press the opening closed and secure with toothpicks to prevent the filling from leaking during cooking.
Mix all dry rub spices together and season both sides of the stuffed chicken. Heat olive oil in a skillet over medium heat and sear the chicken for about 4 minutes per side until golden brown.
Transfer the skillet to a preheated 400°F oven, or move the chicken to a baking dish. Bake for 15–18 minutes until the internal temperature reaches 165°F.
Remove the chicken from the oven and loosely cover with foil. Let it rest for 5 minutes before serving to lock in juices and keep the filling creamy.