Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Butterfly the chicken breasts and pound each to a uniform thickness of approximately 0.25 inches using a meat mallet.
In a small bowl, incorporate the minced garlic and chopped parsley into the softened butter until homogeneous.
Season the flattened chicken with salt and pepper, then spread 1 tablespoon of the garlic-butter mixture over the surface of each fillet.
Place 1/2 cup of mozzarella cheese at one end of each fillet and roll the chicken tightly, securing with toothpicks if necessary.
Prepare a breading station with three separate bowls containing flour, whisked eggs, and a mixture of panko and parmesan cheese.
Dredge each roll in the flour, dip into the egg wash, and coat thoroughly with the panko-parmesan mixture.
Place the rolls seam-side down on the baking sheet and bake for 25 minutes or until the internal temperature reaches 165°F (74°C).
Allow the chicken to rest for 5 minutes before removing toothpicks and serving.