Heat the canola oil in a pan over medium heat. Cook the stuffed chicken for five minutes on each side, until cheese is melted and chicken is cooked through.
On a cutting board, slice a pocket in the chicken horizontally and fill the pocket with a heaping spoonful of the veggie mixture. Press the edges of the chicken together to seal in the filling. Repeat with the remaining chicken.
In a separate bowl, combine the chicken with the salt, chili powder, cumin, and garlic powder, evenly distributing the spices over the chicken.
Heat the canola oil in a pan over high heat. Cook the peppers, onion, salt, and pepper until soft and slightly caramelized. Transfer the cooked veggies to a bowl. In the same bowl, mix in the cream cheese, cheddar, and pepper jack, stirring until evenly incorporated. Set aside.