Place each chicken breast between a sheet of wax paper and pound, using a mallet or rolling pin, to about 1/8 inch thickness; be careful not to 'break' the chicken. Wrap and refrigerate until seasoned butter is frozen.
To Make Seasoned Butter: In a small bowl combine the softened butter, 1/2 teaspoon pepper and 1 teaspoon garlic powder and mix well. Spread mixture into a 2x4 inch rectangle on a piece of aluminum foil; freeze until firm.
When butter is firm, cut into 8 equal size pieces and place one piece on each chicken breast. Fold in edges of chicken and roll to encase butter completely. Secure with toothpicks.
In a small bowl, beat eggs with water. In a shallow dish or bowl, mix together the 1/4 teaspoon pepper, 1/4 teaspoon garlic powder, dill weed and flour. Place bread crumbs in a separate shallow dish or bowl. Dip chicken rolls in seasoned flour, then egg mixture, then crumbs. Place coated chicken in a shallow dish, cover and refrigerate for about 30 minutes.
Heat oil in a large skillet over medium high heat. When oil is hot, deep fry chicken rolls for about 5 minutes, then turn over and deep fry for another 5 minutes until golden and cooked through, with no pink showing inside. Drain on paper towels, garnish with lemon slices and parsley and serve.