In a mixing bowl, combine softened butter, minced garlic, chopped parsley, dill, lemon zest, salt, and pepper. Mix until well combined.
Scoop the herb butter mixture onto a piece of plastic wrap and form it into a log. Wrap tightly and refrigerate for at least 30 minutes until firm.
Preheat your oven to 375°F (190°C).
While the butter is setting, prepare the chicken breasts. Place each chicken breast between two pieces of parchment paper and pound gently with a meat mallet until about ½ inch thick.
Once the herb butter is firm, cut it into 4 equal pieces. Place one piece of butter in the center of each chicken breast.
Fold in the sides of the chicken over the butter, then roll it up tightly from the bottom, tucking the ends in as you go. Secure with toothpicks if necessary.
Set up a breading station with three bowls: one with flour, one with beaten eggs, and one with breadcrumbs.
Dredge each chicken roll first in flour, shaking off excess, then dip in beaten eggs, and finally roll in breadcrumbs until fully coated.
In a large skillet, heat cooking oil over medium heat. Carefully place the chicken rolls in the pan, seam-side down. Fry for about 5-7 minutes on each side, or until golden brown.
Transfer the chicken to a baking dish and bake in the preheated oven for an additional 15-20 minutes, or until the chicken is cooked through and juices run clear.
Let the Chicken Kiev rest for a few minutes before serving.
Notes
Serve on a bed of fresh greens with lemon wedges and extra herbs for garnish.