Preheat oven to 350 degrees. Pound chicken between sheets of wax paper to 1/4" thickness. Pat chicken dry. Combine cheese, green onions and basil in small bowl. Season with salt and pepper. Spread cheese mixture lengthwise over half of each chicken piece. Tuck short ends in. Roll chicken up, starting at one long side, into a tight cylinder. Tie ends with string or spear with wooden toothpick to hold. Dip chicken in egg, allowing excess to drip into bowl. Roll in bread crumbs, shaking off excess.
Place chicken in an 8" square baking dish. Pour 2 tablespoons melted butter over. Bake until cooked through, about 20 minutes.