Microwave the coconut milk in a medium heat-safe bowl until it's warm. It may take about 30 seconds. It should be lukewarm, not hot. Let it cool if it gets too hot.
In a standing mixer with a paddle mixer, combine lukewarm coconut milk and yeast. Let it sit until dissolved (about a minute). Add sugar, salt, and eggs, and continue mixing on medium speed.
Remove the paddle attachment, attach the dough hook, and add flour. Continue mixing for 2-4 minutes until the dough is firm, elastic, and doesn’t stick to the bottom of the pan.
Add half of the butter and continue mixing until the butter has been fully incorporated. You may have to stop the mixer and mix by hand to incorporate the butter thoroughly.
Add the remaining of the butter a little at a time until finished. It is ok if the dough looks loose.
Continue kneading for 4-5 minutes until it is smooth, soft, and shiny. The easiest way to know when the dough is ready is when it slaps against the bowl.
Take out the dough and place it on a lightly floured board. Knead a couple of times, then place brioche dough in a large, greased bowl.
Cover loosely with a clean kitchen cloth and let it rise in a warm, draft-free place for 1-2 hours or until doubled. Punch the dough down.
At this point, the dough maybe be refrigerated overnight or until ready to use. When ready to use, remove and bring it to room temperature to make it workable for 30-60 minutes.
Divide the dough into 16 pieces.