Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish. Using a small, sharp knife, carefully slice a deep pocket into the thickest side of each chicken breast, being careful not to cut all the way through to the other side.
In a medium bowl, combine the shredded mozzarella, chopped pepperoni, 1/4 cup marinara sauce, softened cream cheese, and fresh basil to create the pizza filling. Divide this mixture evenly into four portions.
Season the inside of each chicken pocket with a pinch of the salt, pepper, and Italian seasoning. Stuff each chicken breast with one portion of the pizza filling, using a spoon or your fingers. Press the edges of the pocket closed and secure with 2-3 toothpicks to prevent the filling from leaking.
Set up three shallow dishes: one with the flour, one with the egg beaten with a splash of water, and one with the panko breadcrumbs mixed with the remaining salt, pepper, and Italian seasoning. Dredge each stuffed chicken breast first in the flour, then dip in the egg wash, and finally coat thoroughly in the seasoned breadcrumbs, pressing gently to adhere.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Carefully place the breaded chicken breasts in the hot skillet and cook for 3-4 minutes per side, until the crust is golden brown and crisp.
Transfer the entire skillet to the preheated oven and bake for 18-22 minutes, or until the internal temperature of the chicken reaches 165°F (74°C) on an instant-read thermometer. Let the chicken rest for 5 minutes before carefully removing the toothpicks. Serve warm with the remaining 1/2 cup of warmed marinara sauce for dipping.