Bring eggs and butter to room temperature. Cut the butter roughly into half inch cubes.
Measure out sugar into a small bowl.
Add the coconut milk, yeast and 1 tsp sugar (from the step above) into another small bowl and whisk gently to combine. Set aside for 5-10 minutes to allow the yeast to activate and start to form bubbles. While waiting, continue with next step.
In your mixer bowl, add the eggs and whisk gently. Then add the vanilla, sugar, flour and sea salt. Stir to combine into a shaggy dough.
With the dough hook attachment, knead the dough on speed 1-2 for about 3 - 5 minutes.
Add the butter, in increments, allowing a couple pieces of butter to mix in most of the way before adding in another cube of butter. Continue adding butter slowly over the course of about 10 minutes. If the butter ends up sticking to the sides of the bowl, periodically, scrape down the sides of the bowl and help the butter get incorporated into the dough.
Once all the butter is incorporated, increase the speed of your mixer to 2-3 and continue kneading the dough for another 30-45 minutes to build the gluten. Patience is key!
The dough is ready when it pulls away from the sides of the mixing bowl and starts to look more like a ball. It will be soft, but shouldn’t stick to your hands. Do a window pane test to double check. If the dough breaks immediately when you stretch it, continue kneading the dough.
When the dough if finished kneading, flour your work surface, and turn the dough out onto the floured surface.
Going around the edges of the dough, fold and press in the edges of the dough into the middle of the dough, creating a ball shape.
Carefully pick up the dough and flip the dough so the bottom smooth side is now on top. Place it back into the mixing bowl with smooth side facing up.
Cover the bowl with plastic wrap and place it in a warm spot to rise.
Rise for about 1 hour until doubled in size.
Press down gently with your fist to deflate the dough and turn the dough out onto a lightly floured surface. Fold in the edges, as was done before, pressing them to the center. Carefully flip the dough over with the seam side down, and place the dough into the mixer bowl.
Cover and let it chill in the refrigerator overnight.