In a small bowl, sprinkle yeast over warm water and stir together. let sit until frothy, about 10 minutes.
In a large bowl or the bowl of a large food processor fitted with a dough blade, combine 2 1/2 cups flour, sugar, and salt. Mix in frothy yeast, water, egg, and vegetable oil. Add remaining 1/2 cup flour, as needed, to form a soft and slightly sticky dough. Knead on a lightly floured surface until smooth and elastic. Place in lightly greased large bowl, turning to coat. Cover and let rise in warm place until doubled in size, about 1-1 1/2 hours.
Place dough on lightly floured surface. The buns can be shaped two ways. The easiest way is to divide the dough into 12 equal pieces and roll each piece into a ball. The dough can also be rolled into a long rectangle, then rolled up end to end. Cut the dough into 12 equal pieces. place the pieces into an ungreased rectangle, square, or circle baking pan with deep sides. Cover and let rise until doubled, about 30 minutes.
While the buns are rising, preheat oven to 375 degrees Fahrenheit.
In a small bowl, whisk together coconut milk, water, and sugar.
Pour the coconut sauce over the buns and bake in preheated oven until tops are golden brown and coconut sauce is bubbling, about 30 minutes.
Let cool in pan at least 30 minutes before serving.