In a small bowl, sprinkle yeast over the lukewarm water and stir together. Allow to sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt.
Mix in the softened butter, then the frothy yeast with water until a soft dough comes together.
On a lightly floured surface, knead the dough just until smooth and elastic. Place in lightly greased large bowl, turning to coat. Cover and let rise at room temperature until doubled in size, about 2 hours.
Grease a 9x13 inch (23x33 centimeter) deep baking dish with butter.
Place dough on lightly floured surface. Roll the dough into a long rectangle, then roll up long side to long side to create a spiral.
Cut the dough into 12 equal spiraled rolls. Arrange the rolls in a single layer in the prepared baking dish. Cover and let rise until doubled, about 30 minutes.
Preheat oven to 400˚F (200˚C).
In a small bowl, whisk together the coconut milk, water, and sugar until well combined.
Pour the coconut sauce evenly over the tops of the buns and bake in preheated oven until golden brown and coconut sauce is bubbling, 25-30 minutes.
Remove the pan from the oven and cover with a piece of foil. Allow to cool covered in the pan for 30 minutes-1 hour before serving.