Preheat oven to 350°. Line a baking sheet with parchment paper.
Combine sugar and 1 cup coconut in the bowl of a food processor; process until finely ground. Combine coconut mixture, flour, baking powder, baking soda, and salt in the bowl of a stand mixer fitted with a paddle attachment. Whisk eggs in a small bowl. Remove 1 tablespoon egg and combine with 1 tablespoon water in a small bowl; set aside. Add butter, remaining eggs, and vanilla to flour mixture; mix at low speed until almost combined. Add almonds and 1/2 cup coconut flakes; mix until just combined.
Divide dough into 2 (8- x 4-inch) loaves on prepared baking sheet. Brush loaves with egg-water mixture. Bake 35 minutes or until lightly browned. Let stand 15 minutes.
Decrease oven temperature to 325°. Cut each loaf crosswise into 16 (1/2-inch) slices. Arrange slices, cut sides down, on baking sheet. Bake 25 more minutes or until lightly browned. Let cool completely.
Whisk together coconut milk and powdered sugar in a medium bowl until smooth. Spread mixture over 1/3 of each biscotti; sprinkle biscotti evenly with remaining 1 cup coconut flakes.