For the yeast:
In a small bowl, combine warm water, yeast, and sugar. Stir to dissolve the yeast as best you can and set aside until yeast is foamy. This should take about 5 minutes or so.
Make the dough:
In a bowl of an electric mixer fitted with a paddle attachment, add the flour, butter, brown sugar, and salt. Mix on low for a few seconds to combine. Stop the mixer and add the yeast mixture, eggs yolks, milk, coconut milk, Coco Lopez, and unsweetened coconut cream. Mix on medium to combine. Scrape the dough from the mixer and dump onto a lightly floured surface. Knead until the dough is smooth and elastic, sprinkling lightly with flour as needed. The dough should feel slightly tacky to the touch, but not sticky, about 5-8 minutes. Be sure not to over flour the dough or the buns will be hella tough. Alternatively, you can mix the dough in your stand mixer using a dough hook over medium speed until the dough is smooth and elastic.
Butter a large bowl, and shape the dough into a ball. Place the ball of dough inside the bowl and turn it a couple of times to coat with butter. Cover the bowl with plastic wrap of a damp dish towel and allow it to rise for about an hour in a warm place until doubled in volume. This may take longer if your area is not warm. While your dough is rising, make the filling:
Make the filling:
In a medium bowl combine the brown sugar and spices in a medium bowl. Remove about 1/4 cup of spiced sugar and set aside. Melt the butter and add the Coco Lopez and dark rum. It’s OK if it doesn’t homogenize. It’s all going to the same place. Set aside.
Roll and cut the buns:
Remove dough from the bowl and turn onto a lightly floured surface. Press the dough down with your hands and shape it into a rough square. Roll or press the dough into a 12x18 rectangle, lifting the dough every so often to make sure it doesn't stick. Lightly sprinkle flour as needed. If your rectangle is longer or shorter than 12x18, don't sweat it. Brush the dough with the melted butter mixture, then sprinkle the spiced sugar mixture. Sprinkle with sweetened coconut flakes. Starting from the long side, roll the dough into a cylinder. Place the dough seam side down onto your surface and cut into about 15 slices.
Preheat your oven to 375 degrees Fahrenheit.
Heavily butter either a 12 inch cast iron skillet or a 9x13 pyrex dish. Sprinkle the reserved 1/4 of cinnamon sugar. Place the dough slices, cut side down on the skillet or pyrex dish. You can crowd them, it's ok. Cover with a damp towel or plastic wrap and allow to rise slightly in a warm place for about 30-45 minutes.
Bake the buns:
Place the buns in the preheated oven and bake until the tops are golden brown, about 20-25 minutes. About 5 minutes before the buns are due to come out of the oven, make the glaze.
Make the glaze:
In a medium bowl, combine the confectioners' sugar, coconut milk, Coco Lopez, spices, dark rum, and vanilla bean paste. Mix until smooth and combined.
Glaze the buns:
Remove buns from the oven and allow to cool slightly, about 5 minutes or so. You can either remove the buns from the cast iron skillet or Pyrex dish and glaze, or you can glaze in the vessel. Whatever floats your boat. Spoon or spread the glaze on top of the buns. Go in on those bad boys.
Sticky buns are best eaten the day they're made, but if you plan eating them the next day, place in the microwave for a few seconds to soften.