Preheat barbecue on MEDIUM for 10 minutes. Meanwhile, scrub potatoes thoroughly to clean. Puncture several times with a fork and wrap individually in aluminum foil. Place on grill and cook with lid closed for approximately 40 minutes.
Cajun Butter: Combine all ingredients in a medium bowl. Stir with a wooden spoon until thoroughly blended. Place Cajun Butter onto a large sheet of waxed paper and shape into a log. Refrigerate and cut into patties when chilled.