Combine 2 tablespoons butter, dill, 1/8 teaspoon salt, pepper, and garlic in a small bowl, stirring well. Chill 1 hour.
Slice chicken breast halves lengthwise, cutting to, but not through, other side. Open halves, laying chicken flat. Place each chicken breast half between two sheets of plastic wrap; pound to a 1/4-inch thickness using a meat mallet or small heavy skillet.
Place about 1 1/2 teaspoons butter mixture on the small end of each chicken breast half, and roll up jelly-roll fashion. Tuck in sides, and secure each roll with wooden picks. Sprinkle chicken evenly with 1/2 teaspoon salt.
Combine 2 tablespoons water and egg whites in a shallow dish, stirring with a whisk. Place bread in a food processor; pulse 10 times or until coarse crumbs measure 3 cups. Microwave 2 1/2 teaspoons butter at HIGH 15 seconds or until melted. Combine melted butter and breadcrumbs in a shallow dish; toss well. Dip 1 chicken breast half in egg white mixture; dredge in breadcrumb mixture. Dip chicken breast half in egg white mixture again; dredge in breadcrumb mixture again. Repeat procedure with remaining chicken breast halves, egg white mixture, and breadcrumb mixture. Place chicken breast halves, seam sides down, in a jelly-roll pan coated with cooking spray. Cover and refrigerate 1 hour.
Preheat oven to 425°.
Bake chicken at 425° for 35 minutes or until the chicken is done. Remove wooden picks before serving.
Place potatoes on a baking sheet coated with cooking spray; coat potatoes with cooking spray. Sprinkle potatoes with remaining 1/8 teaspoon salt; toss. Bake potatoes at 425° for 40 minutes or until tender, turning once after 30 minutes. Transfer potatoes to a bowl, and toss with remaining 2 teaspoons butter. Serve with chicken.