Preheat the oven to 400°F (204°C) and prepare a baking sheet.
Butterfly each chicken breast by slicing lengthwise about 3/4 of the way through to form a pocket without cutting all the way through.
In a bowl, combine the cream cheese, shredded cheddar, and diced jalapeños until smooth.
In a separate bowl, whisk the egg with 1 teaspoon salt and 1 teaspoon ground black pepper to make the egg wash.
In a third bowl, mix the panko breadcrumbs with 1/2 teaspoon paprika.
Spoon the jalapeño-cheese mixture into each chicken pocket and secure the opening with toothpicks.
Lightly season the outside of each stuffed breast with salt and pepper, dip first into the egg wash, then press into the breadcrumb mixture to coat.
Place the coated chicken breasts on the prepared baking sheet and brush the tops with the melted butter.
Bake for about 22 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the coating is golden.
Remove toothpicks before serving and serve hot.