Pre-heat the oven to 400. Line a baking sheet with parchment paper and set aside.
In a mixing bowl, combine the cream cheese, mayo, cheddar, pimientos and a sprinkle of garlic powder and onion powder and mix together until well combined.
Place the chicken breasts on a cutting board. Using a sharp knife, slice the breasts from the side (creating a top and bottom) almost all the way through. Open each breast at the slit and distribute the pimento cheese mixture evenly between the breasts, placing it inside the open chicken. Spread cheese across the surface and close the breast, folding the top half back over the pimento cheese.
Combine the flour and Cajun seasoning in a small dish and stir together. Place the stuffed breasts in a Ziploc bag and add the Cajun flour mixture. Lightly flip the bag around until chicken is coated with flour. Place the beaten egg white in a shallow dish and the panko crumbs in a second shallow dish. Remove each stuffed breast from the flour bag and dip it in the egg white, turning to coat. Then move the coated breast to the dish of panko crumbs and coat it on all sides.
In a large skillet, add the oil and bring over medium-high heat. Add the stuffed and coated chicken breasts to the pan and cook for about 1 minute until the bread crumbs on the bottom are golden. Flip the breasts and cook for another minute on the other side. Transfer the breasts to the prepared baking sheet and place in the pre-heated oven. Bake for 30-35 minutes until chicken is fully cooked through.