Wash and dry the potatoes and then wrap them individually in sheets of aluminum foil.
Prepare a bull's-eye fire for medium heat (see below). When the coals are ready, place the sweet potatoes directly on the charcoal grate resting on the edge of the charcoal. Close the lid and cook until the potatoes are soft, 45 to 55 minutes, turning them occasionally. To check for doneness, squeeze the potatoes with a pair of tongs.
Remove the potatoes from the grill and let them cool for about 15 minutes before unwrapping them. Slit the skins with a knife and peel off and discard the skin. Cut the flesh into ½-inch cubes. Set aside while you make the glaze.
Place a 12-inch cast-iron skillet over direct medium heat Coconut-Glazed Sweet Potatoes (you can also do this step on your stove top). Combine the glaze ingredients in the skillet and bring the mixture to a simmer, stirring occasionally. Let the mixture reduce until half the volume remains, 5 to 8 minutes, stirring occasionally. The glaze will be slightly thick. Remove the skillet from the heat and add the sweet potato cubes, gently stirring to coat with the glaze, being careful not to mash them.
In a small skillet over high heat, toast and brown the coconut, about 2 minutes.
Place the potatoes in a serving bowl and sprinkle the toasted coconut over the top. Serve warm.