Make and the chill the garlic butter before even heating the grill. Mash together the butter, garlic, parsley, pepper, and lemon juice until well combined. Form the butter mixture into a rough log shape on a piece of parchment paper and roll into a tight cylinder. Freeze the butter mixture while you butterfly the chicken.
Remove the chicken breast from the fridge and pat dry with paper towels. Use a sharp knife to butterfly the breast — place your hand on the breast and slice through it starting at the thickest part to slice it in half horizontally. Cover the breast with plastic wrap or use a zip-top bag and use a mallet to pound the thickest sections to about ¼ inch thickness. Season the pieces on all sides with salt and pepper.
Cut a few large pieces off the frozen butter log and place these in the center of the each chicken breast. Fold sides in over the butter, then roll the chicken up starting from the bottom, secure the seam with two toothpicks. Chill the chicken breast while you heat a grill.
Heat a gas or charcoal grill to medium high heat, aiming for about 400 degrees F. While the grill heats, prepare the breading situation for the chicken. Place the flour in a large bowl and season with salt and pepper. Whisk the eggs with salt and pepper in a medium bowl. Season the breadcrumbs with salt and pepper and place in their own medium bowl.
When the grill is good and hot. Remove the chicken from the fridge and coat like this — flour, egg, breadcrumbs. Place the chicken pieces seam side down in a skillet. Roast the chicken keiv for 20 to 25 minutes until golden brown. Top the finished keiv with more of the garlic butter and parsley for serving.