For filling, in a medium skillet, heat the 1 tablespoon butter over medium heat. Add mushrooms and onion; cook until tender. Stir in crabmeat, crackers, parsley, salt, and pepper. Stir in 2 tablespoons of the sauce. Place about 1/4 cup of the filling on each piece of chicken. Fold in sides; roll up. Secure with wooden toothpicks, if necessary. In a large skillet, heat the 2 tablespoons butter over medium heat. Cook chicken rolls, half at a time, in hot butter until brown on all sides.
Arrange chicken rolls, seam sides down, in an ungreased 3-quart rectangular baking dish
. Top with the remaining sauce. Bake, covered, about 35 minutes or until chicken is no longer pink. Sprinkle with cheese and paprika. Bake, uncovered, about 2 minutes more or until cheese is melted. Remove toothpicks, if using.