In a small bowl, mix softened butter, garlic, parsley, herbs, salt and pepper. Shape into a log, wrap, and chill at least 30 minutes.
On a cutting board, lightly pound each chicken breast to about 1⁄4‑inch thickness, keeping one side thicker.
Place a portion of herbed butter in the center of each breast. Fold sides over and roll up tightly to enclose the butter fully. Secure with toothpicks if needed.
Coat each breast in flour, shaking off excess. Dip into beaten eggs, then coat evenly with breadcrumbs. Chill 15–20 minutes to help maintain shape.
Preheat oven to 375 °F (190 °C). In an oven‑safe skillet, heat oil or clarified butter over medium‑high heat. Sear roulades 2–3 minutes per side until golden brown.
Transfer skillet to oven and bake 15–20 minutes (internal temp 165 °F) until cooked through and butter fully melted inside.
Remove toothpicks, let rest 5 minutes, then slice or serve whole with pan juices spooned over.