Cut 1 stick unsalted butter into ½-inch cubes. Place in a medium bowl and let sit at room temperature until softened, about 45 minutes.

Prepare the following, adding each to the butter as you complete it: Finely chop 1 tablespoon fresh parsley leaves until you have 1 tablespoon, plus more for garnish. Finely chop 1 small bunch fresh chives until you have 1 tablespoon. Mince 2 garlic cloves. Add ¼ teaspoon kosher salt and mix until well-combined.

Spoon the butter onto a piece of plastic wrap and roll into a 1-inch-thick log. Wrap tightly and freeze until firm, at least 30 minutes.

Meanwhile, pound 4 boneless, skinless chicken breasts: Working with 1 chicken breast at a time, place inside a gallon zip-top bag and seal the bag, pressing out as much air as possible. Pound the breast and the tender if attached with a rolling pin, small skillet, or the flat side of a meat mallet to an even ¼-inch thickness. Take care not to split or break apart the chicken breast.

Remove the butter from the freezer. Cut in half lengthwise, then cut each piece in half crosswise, for 4 even pieces.

Roll and wrap one piece of chicken at a time: Place one piece on a sheet of plastic wrap. Season all over with ¼ teaspoon of the kosher salt and a few grinds black pepper. Place a piece of compound butter in the center of the chicken breast. Trim the any ragged edges off the chicke if needed, and place the on the butter. Using the plastic wrap as a guide and starting with a long side, tightly roll up the chicken, tucking the short sides in as you go. Tightly twist the ends of the plastic wrap to create a log shape. Repeat with the remaining chicken breasts.

Place the wrapped chicken seam-side down on a plate. Freeze until the bottoms are slightly firm and hold together, about 30 minutes. The chicken should not be frozen solid. Meanwhile, arrange a rack in the middle of the oven and heat oven to 400ºF. Fit a wire rack inside a rimmed baking sheet.

Place 1 ½ cups panko bread crumbs in a shallow bowl or pie plate. Place ½ cup all-purpose flour on a large plate. Whisk 2 large eggs and 1 tablespoon water together in a second shallow bowl until evenly combined.

Unwrap the chicken. Working with one piece at a time, dredge completely in the flour, then dip into the egg, and finally thoroughly coat with the breadcrumbs. Return to the plate.

Heat ½-inch vegetable oil in a large cast iron skillet (about 4 cups in a 12-inch skillet) to 350ºF. Add 2 chicken breasts and cook until golden-brown all over, 2 to 3 minutes per side. Transfer to the rack and repeat with the remaining 2 pieces of chicken. The chicken will not be cooked through.

Bake until the chicken is cooked through and registers 165ºF on an instant-read thermometer, 12 to 15 minutes. Let cool 5 minutes before serving. Garnish with the parsley.