In a bread machine, combine the large egg, chilled milk, high-gluten flour, sugar, and yeast. Knead the mixture for about 5–6 minutes until well combined and slightly elastic.

Add the softened butter and salt to the dough. Knead for an additional 10 minutes until the dough becomes smooth and elastic in texture.

Shape the dough into a ball and place it in a lightly greased bowl. Cover and let it rise in a warm area until it has doubled in size, which should take roughly 1 hour.

While the dough rises, mix the black sesame powder, coconut oil, and sugar with the water to create a spreadable filling. For the crumble topping, rub the flour and sugar with the coconut oil until it becomes crumbly and textured.

Once the dough has risen, roll it out on a lightly floured surface. Spread the black sesame filling evenly over the surface. Fold the dough, cut it into strips, then roll the strips together and place them in a greased pan.

Allow the assembled dough to rise again in a warm area until it puffs up, which will take about another 30 minutes.

Brush the top of the risen loaf with a beaten egg and sprinkle the crumble topping over it. Bake in a preheated oven at 350°F for about 30 minutes, or until the top is golden brown.

After baking, let the loaf cool in the pan for about 5 minutes before transferring it to a wire rack to cool completely. Slice and enjoy!