Heat oven to 375 degrees F. Spread out 1/2 cup coconut on a baking sheet and bake, stirring once, until golden brown, about 9 min; set aside.

Brush six 4-inch (or one 8-inch) bundt pans with butter and generously dust with granulated sugar, tapping out excess; set aside.

Process together flour, remaining 1/2 cup coconut, the salt and baking soda in a food processor until coconut is very finely chopped.

In a mixer bowl, beat together butter and granulated sugar on medium speed until light and fluffy. Beat in eggs until combined well. Alternately beat in flour mixture and coconut milk in three batches, beginning and ending with flour mixture, scraping down sides of bowl, until combined well. Divide batter among prepared pans and bake until golden and a toothpick inserted in center comes out clean, about 25 min for 4-inch cakes (or about 35 min for 8-inch cake). Transfer cakes in pans to a wire rack and cool 5 min. Remove cakes from pans and let cool completely.

Meanwhile, for icing, whisk together confectioners' sugar and 2 tbsp water until smooth.

To serve: Drizzle cakes with icing and sprinkle with toasted coconut. Makes six 4-inch mini cakes (or one 8-inch cake).