How to Make It
If using alligator pepper pod, crack open alligator pepper pod by pressing down on the pod with the flat side of your palm. Remove the seed pods from their shell. Separate the seed pods (there should be 3) and break to remove the seeds. Rub the pod pieces between your fingers onto a small baking sheet to separate the shaft from the seeds. Discard the shaft, and add seeds to a spice grinder. Process alligator pepper seeds or grains of paradise in a spice grinder until finely ground, about 15 seconds. Reserve about 3 1/2 teaspoons ground pepper; reserve remaining pepper for another use.
Using a rubber spatula, fold together ground grains of paradise, chopped lime segments, butter, lime leaves, garlic, shallot, parsley, thyme, and sea salt until thoroughly blended. Transfer the butter into a serving vessel, and serve immediately. To store, spoon butter mixture onto a sheet of plastic wrap, roll into a log, and keep refrigerated for up to 1 week. Freeze, wrapped in plastic wrap, up to 1 month. Use this butter as a rub on meat or seafood before cooking, stir into steamed rice, or toss with warm roasted vegetables.