Make the dough: In a large bowl, mix the yeast with the sugar. Stir in the warm milk and let rest for 5 minutes. Stir in the egg, then the flour, coconut milk, and butter. Knead the dough and let rest in the bowl, covered with a warm, wet towel in a warm place until doubled in volume, about 1 hour.
Then prepare the filling: Mix the coconut, condensed milk, vanilla, and nutmeg together in a medium bowl. Reserve!
Roll out the dough on a floured surface to form a 15-inch rectangle, then brush most of the melted butter on top of the dough and spread the filling. Sprinkle brown sugar on top, distributing evenly. Roll up tightly like a cinnamon roll log and cut into 12 slices.
Grease and line with parchment paper a 13” x 9” rectangular baking pan. Arrange the coconut rolls into the pan in a single layer, keeping them about at least 1-inch apart. Brush the remaining melted butter on top of the rolls, and let rest at room temperature for 30 minutes as they will continue to rise.
If you are using a store-bought refrigerated crescent roll dough, try to roll out the dough on a floured surface as a whole as you can and then mend the pieces together forming a rectangle. Follow the same directions to fill it, roll it up into a log, cut, and brush with melted butter. There will be no need to wait for 30 minutes because they will not rise! In fact, you will save more than 90 minutes because you won’t prepare the dough from scratch and wait to rise it two times.
Bake in a preheated oven for about 25-30 minutes at 390° F (200° C) if the dough is from scratch or at 350° F (180° C) if the dough is pre-made. Cover loosely with a sheet of aluminum foil for the last 15 minutes, especially if the dough is homemade. You don’t want them to brown too much on top. They are ready when puffy and golden brown!
Meanwhile, make the topping or coconut frosting. Using an electric mixer, beat together the cream cheese, butter, and powdered sugar until smooth (no lumps). Then beat in the sweetened condensed milk and coconut milk. If you want, stir in coconut extract. Spread evenly the frosting over the warm coconut rolls and then sprinkle coconut flakes on top. Enjoy!