Combine mustard through lime zest in a small bowl. Pour over the whole trout. Marinate in the refrigerator for 30 minutes.
Prepare grill to 350-400 degrees. Place soaked plank on grill grates and close lid. Heat plank for two to three minutes or until a light smoke develops. Flip plank and place fish on heated side of plank (reserve remaining marinade.)
Grill with lid closed for 8 to 10 minutes. Open lid and drizzle with remaining marinade. Close lid and continue to cook for an additional 8 to 10 minutes or until trout is medium done.
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