Combine lukewarm water and sugar in a container.

Add dry yeast to the water-sugar mixture.

Mix well and let proof for 10 minutes.

Sift cake flour, bread flour, baking powder, sugar, and salt into a large bowl.

Add the yeast mixture and lukewarm milk to the dry ingredients and mix.

Knead the dough 100 times, pressing, stretching, and folding.

Incorporate lard (or butter or shortening) in 3 batches, kneading after each addition.

Shape the dough into a ball and place in a lightly oiled bowl.

Cover with plastic wrap and let rise in a warm place until doubled in volume (approximately 40 minutes at 35C).

Deflate the dough on a work surface.

Divide the dough into 6 equal portions.

Form each portion into a ball, cover with a damp towel, and let rest for 20 minutes.

Prepare the meat filling by combining ground pork, mushroom soaking water, Shaoxing wine (or sake), soy sauce, grated ginger, sesame oil, tianmiangjiang (or miso), katakuriko, grated garlic, sugar, and salt in a bowl.

Mix the filling ingredients thoroughly.

Divide the filling into 6 portions.

Roll out each dough portion into a 7mm thick circle.

Roll it out a bit more to form a 10cm square.

Place a portion of the filling in the center of each dough square.

Bring two opposing corners together above the filling and pinch to seal.

Repeat with the other two corners.

Pinch the remaining corners together and twist the top to close securely.

Let the formed buns rise again for 10 minutes.

Steam the buns for 25 minutes using an oven's steam function, or 15 minutes in a steamer, ensuring ample space between them.

Alternatively, pan-fry the buns by heating oil in a frying pan.

Cook the buns with a lid on over very low heat for 3 minutes.

Add some boiling water to the pan and steam-cook for another 10-12 minutes.

Note: This cooking time applies to making 12 buns (if you choose to divide the dough into 12 portions instead of 6).