In a small bowl, combine the softened butter, dried chives, and minced garlic. Shape the butter mixture into a rectangle approximately 2 × 3 inches. Wrap tightly in plastic wrap and freeze for 30 minutes.
Preheat the oven to 425°F.
Place each chicken breast between two pieces of plastic wrap. Using the flat side of a meat mallet, gently pound the chicken until it is about ¼-inch thick.
In a small bowl, combine the garlic powder, salt, and black pepper. Season both sides of each chicken breast with the seasoning mixture.
Remove the chilled butter from the freezer and cut it into four equal pieces. Place one piece in the center of each chicken breast.
Fold the chicken tightly around the butter, bringing the sides toward the center to completely enclose the butter. Secure with toothpicks to help hold the chicken together.
Crush the gluten-free cornflakes. In a shallow bowl, combine the crushed gluten-free cornflakes, dried parsley, and paprika.
Pour the milk into a separate shallow bowl. Dip each chicken breast into the milk, then roll it in the cornflake mixture, coating all sides.
Place the breaded chicken seam-side down on a parchment-lined baking sheet.
Bake for approximately 35 minutes, or until the chicken reaches an internal temperature of 165°F.
Carefully remove the toothpicks before serving.