Start with the tangzhong by placing bread flour and milk in a saucepan. Heat over medium-high heat and whisk until it comes together, about 1 minute. Set aside and allow to cool.

Combine the yeast and milk and let it rest for 5 minutes, allowing the yeast to become active. Combine the bread flour, cake flour, salt, and sugar in a large bowl of a stand mixer. Add the tangzhong, milk, 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. Prepare a baking sheet by placing parchment paper down.

Divide the dough into 6 equal portions. Shape into round balls. Take one of the balls and roll it out to a 8-inch by 8-inch square. Take the bottom part of the rolled up dough and tightly roll the dough until it forms a cylinder. Pinch the edges together and roll in on the table until the cylinder is mostly smooth. The koppepan should be about 8 - 9 inches long. Transfer to the baking sheet, seam side down. Cover with plastic wrap and let rest for 30 – 60 minutes, or until doubled in size.

Preheat an oven to 375°F. In a small bowl, whisk an egg and 2 tablespoons of milk. Remove the plastic wrap from the baking sheet and brush each of the buns with egg wash. Place in the oven and bake for 15 to 20 minutes or until golden brown.