To the sponge, add 1 cup flour, 3 tablespoons vegetable oil, 1 teaspoon salt1 tablespoon sugar and ¾ cups unsweetened shredded coconut.
Attach to the mixer and, using the dough hook, start mixing everything, adding 3 more cups of flour, ½ cup at a time. After 3 or 4 minutes of kneading, the dough should be soft but not sticky. If needed, add up to an extra ½ cup of flour. But don't end up with a dry dough. I used 4 cups total in my recipe.
If kneading by hand, do so for 5 to 7 minutes on a clean surface, lightly flouring as necessary after the dough comes together.
Transfer dough to a greased deep bowl, turn to grease on all sides, cover with plastic wrap and let stand in a warm place until doubled, about 1 ½ to 2 hours.
Gently deflate the dough with your fist and dump it onto a lightly floured surface. Give it a few kneads and divide it into 12 equal pieces of dough using a kitchen knife or dough scraper. The amount can vary if you want more smaller buns or fewer larger ones. You can also weigh the whole dough, divide it by the amount of rolls you want to make, and weigh each piece to have very even buns; I never bother to do that, I just eyeball it. Shape each piece into a ball, pinching the bottom. Cover it with the palm of your hand, and, moving your hand counterclockwise to your left (or the other way, it doesn't matter), shape them into balls, as tight as you can.
Grease a baking pan, and put the dough balls next to each other, barely touching. Cover with a clean, dry towel and let rise until almost doubled, about 30 to 40 minutes.
Preheat the oven to 400ºF/200°C about 20 minutes before baking.
Bake the buns for 20 to 25 minutes, until the tops are dry and golden and the rolls sound hollow when lightly tapped on the bottom.
Let cool on a wire rack.