Preheat the oven to 350°. Line 2 large cookie sheets with parchment paper and brush with 2 tablespoons of the clarified butter.
In a medium bowl, thoroughly mix together the coconut, sugar, egg whites, flour and the remaining 1/4 cup clarified butter.
Drop about 1 1/2 tablespoons of the coconut mixture onto a prepared cookie sheet. With dampened fingers, pat the mixture into a thin, flat, 6-by-3-inch triangle. Repeat with the remaining coconut mixture.
Bake 1 sheet of cookies at a time for 12 to 15 minutes, or until the tuiles are golden. Let them cool completely on the pan.
The coconut tuiles can be made up to 3 days ahead and stored in an airtight container.