In a medium bowl, combine butter, parsley, garlic, salt, and pepper. Form into a log and wrap with parchment paper, waxed paper, or plastic wrap. Refrigerate for at least 2 hours, until firm.
Place the chicken breast in a zip-top bag and pound with a meat mallet until the chicken is ¼” thick.
Place butter in the center of each chicken breast and wrap tightly from the long side, tucking in the short sides as you go. Secure with toothpicks. Wrap tightly with plastic wrap and refrigerate at least 2 hours or overnight.
In a shallow bowl, combine almond flour, parmesan, and cayenne pepper.
In another bowl, beat the eggs.
Coat the chicken in the eggs, and then dip in the almond flour mixture, using your fingers to press to coating into the chicken.