Pour warm coconut milk into a bowl. Add sugar and yeast, stir once, and let sit for 10 minutes until foamy.
In a large bowl, mix the flour and salt evenly.
Make a well in the center of the flour. Add butter, yeast mixture, and eggs if using. Mix until a rough dough forms.
Transfer dough to a lightly floured surface. Knead for 5 to 7 minutes until soft and smooth.
Place dough in a lightly oiled bowl. Cover and let rise in a warm place until doubled in size, about 1 hour.
Gently punch down the dough. Divide into equal portions and shape into rolls or loaves.
Place shaped dough on a baking tray. Cover and let rise again for 30 to 40 minutes until puffy.
Preheat oven to 350°F (175°C). Bake for 25 to 30 minutes until golden brown and hollow sounding when tapped.
Remove from oven and immediately brush tops with butter. Let cool slightly before serving.