Stir together mayonnaise, mustard, and honey. Brush one side of each fillet with about 1-1/2 teaspoons of the mustard mixture. Sprinkle fillets with pecans, parsley, and carrot. Roll fish up jelly-roll style. Secure with wooden toothpicks that have been soaked in water. Tear off a 24x18-inch piece of heavy foil. Fold in half crosswise. Trim to make a 12-inch square. Cut several slits in foil. Place fish rolls on foil.
Arrange preheated coals around a drip pan in a covered grill. Test for medium heat above pan. Place foil with fish rolls on grill over drip pan. Cover and grill for 14 to 16 minutes or just until fish begins to flake easily when tested with a fork. Brush remaining mustard mixture on rolls; sprinkle with parsley. Makes 4 servings.