Preheat oven to 375F. Line two standard muffin tins with 18 paper liners and set aside.
In a medium bowl whisk together rice flour and baking powder. Set aside.
In the bowl of a stand mixer, beat the butter until smooth. Slowly add in the sugar and continue mixing on low until fluffy. Add eggs, one at a time, beating well after each addition.
Pour the dry ingredients into the wet ingredients and mix well. Stir in the coconut milk until combined. Add the grated coconut and cheddar cheese and stir just until combined.
Spoon the batter into the prepared muffin cups, filling each cup about 3/4 full. Bake 20 to 25 minutes, or until the muffins are lightly browned and toothpick inserted in middle comes out clean.
Remove muffins from oven. Brush each muffin top with butter while still warm and sprinkle with grated coconut or some sugar. Serve warm.