Wash the kale thoroughly and cut out the stalks. Cut the wide leaves into strips the width of the small leaves.
In a large pot set over a low flame, heat the coconut milk until it is thoroughly mixed and just lukewarm. Transfer to a large, nonreactive bowl and add the remaining ingredients. Stir in the kale, cover with plastic wrap and refrigerate for at least 4 hours
Preheat a grill or a cast-iron grill pan over high heat. Remove the kale from the refrigerator and stir to make sure the leaves are well covered in marinade. Using metal tongs, place the kale on the grill in a single layer. Cook for 45 to 60 seconds, or until the leaves are sizzling, then turn over and grill the other side for another 45 to 60 seconds, or until the leaves have visibly softened. Serve immediately