Place the first 7 ingredients in a pot and whisk to combine. Set over medium-heat, bring to a simmer, and simmer for 1 minute. Remove curry sauce for the heat and set aside for now.
Preheat the oven to 375°F. Using a sharp knife carefully cut the crab legs, widthwise, into 2" to 4" pieces. Use kitchen scissors to cut off the top part of the shell on one side of each piece to expose the crabmeat. Arrange the crab pieces, exposed meat side up, in a 13" x 9" baking dish.
Pour the curry sauce over the crab. Cover the pan with aluminum foil and bake 12 to 15 minutes, or until the crab is steaming hot. Sprinkle the crab, to taste, with cilantro leaves and chilies and coconut, if using, and then serve.