In a medium bowl, mash a softened butter with a fork. Add minced dill, salt and pepper. Shape it into a log, cover with a plastic wrap and freeze for 30 minutes.
Remove tenderloins from each chicken breast and lay them on a piece of plastic wrap. Lightly pound a tenderloin, being careful not to tear the meat. They need to be approximately ⅛" thick.
Pound chicken breasts to the same thickness. Salt and pepper each chicken breast.
Cut a butter log into 4 equal pieces. Place one piece of it onto a centre of chicken breast and cover it with a tenderloin. Fold in the ends of chicken breast and roll breast into a log, making sure to completely cover the butter; roll tightly. Refrigerate the rolls for at least 30 minutes.
Preheat the oven to 350 F.
Whisk milk, eggs, salt and pepper together in a shallow bowl. Put flour in a second bowl and Panko breadcrumbs in a third shallow bowl.
Dredge each Chicken Kiev in flour and dip in the egg and milk mixture. Then roll it in breadcrumbs. Repeat the step with egg and breadcrumbs (without dredging in flour).
Heat oil in a large skillet and over medium-high heat. The oil should be enough to cover chicken half way. Fry chicken on both sides until golden, about 5-7 minutes. Transfer it onto a prepared baking dish. Bake for 15-20 minutes.