Combine 3 tablespoons coconut milk and 1/3 cup bread flour in a small pan. Heat over medium-high heat and whisk until it comes together, about 1 minute. Set aside and allow to cool.

Combine the yeast and remaining coconut milk and let it rest for 5 minutes, allowing the yeast to become active. Combine the remaining bread flour, sugar, salt, and cardamom in a large bowl of a stand mixer with a dough hook. Add the mixture in the pan, the yeast milk mixture, vanilla paste, and egg to the bowl and mix until it just comes together.

While the dough begins to knead, add the butter one tablespoon at a time. Knead the dough for 5 minutes. If the dough is too sticky, add 1 tablespoon of flour at a time. If it is too dry, add one tablespoon of milk at a time.

Transfer to an oiled bowl, cover, and let rest for 1 hour or until it has doubled in size. Once doubled, punch down and knead. Divide the dough into 8 equal portions, shape into a ball, and cover with a kitchen towel.

Take one of the portions and roll it out into an oval shape. Take the dough and tightly roll it up.

Shape into a round ball and place back under the kitchen towel. Repeat this and the previous step until all the portions have been shaped into balls.

Prepare a 9 inch cast iron pan by rubbing the interior with butter. Place one of the balls in the center of the pan. Place the remaining 7 around it, spacing them evenly. Cover with a kitchen towel and let rest for 30 to 60 minutes, or until doubled in size.

Preheat an oven to 350°F. Remove the kitchen towel from the pan. In a small bowl, whisk together the egg and coconut milk until well combined. Brush the top of the rested buns with the egg wash. Place in the oven and bake for 18 to 22 minutes, or until golden brown and cooked through.