Place chicken between layers of wax paper. Using a meat mallet, pound each breast out to 1/8 inch thick.
In a small bowl, combine fresh herbs, chopped green onion, and minced garlic. Sprinkle mixture evenly over flattened chicken breasts and season with salt & pepper.
Cut butter into fourths lengthwise and place one piece of butter in the middle of each chicken breast.
Fold in the sides, then roll each breast tightly and set on a plate, seam-side down.
Measure flour, beaten egg + water, and bread crumbs all out into separate bowls.
Dip chicken in flour to coat, then egg + water mixture, and finally bread crumbs.
Cover and chill for at least 1 hour or up to 24 hours.
Remove chicken from refrigerator when ready to use; preheat oven to 400° F.
In an oven-proof skillet, heat 1 Tablespoon olive oil and 1 Tablespoon butter on medium high.
Add chicken and cook on each side until golden brown (5-10 minutes per side).
Transfer skillet to pre-heated oven and bake for 18-20 minutes, until chicken is no longer pink inside.
Spoon drippings from pan over rolls; garnish with additional fresh herbs, salt and pepper.