Sweet Coconut Buns

Name: Sweet Coconut Buns
Ingredients: For the bun dough; 1/2 cup unsweetened coconut milk from a 13.5 ounce can ( make sure to whisk the can of milk thoroughly) and save the rest for the sauce; 1 tablespoon active dry yeast; 3 tablespoons granulated sugar; 1 3/4 cups bread flour, divided (plus more for kneading); 1 room temperature egg, slightly beaten; 1/2 cup sweetened coconut flakes; 2 tablespoons very, very soft butter; A pinch of salt; For the sauce and baking; The remainder of the can of coconut milk; 1/4 cup water; 4 tablespoons granulated sugar