Prepare Tangzhong: In a medium saucepan, whisk together 1/2 cup all-purpose flour, 1/2 cup milk, and 1/2 cup water. Cook over low heat until thickened, about 3-5 minutes. Let cool to room temperature.

Mix Dough: Combine cooled Tangzhong with active dry yeast, sugar, an egg, honey, salt, and 2.5 cups of all-purpose flour in a large bowl. Mix until a shaggy dough forms.

Knead: Transfer dough to a floured surface or stand mixer. Knead for 10 minutes or until smooth and elastic.

First Rise: Place dough in a greased bowl, cover, and let rise until doubled in size, about 1-2 hours.

Shape Buns: Punch down dough, divide into 16 portions, and shape into balls. Place on a lined baking sheet.

Second Rise: Cover shaped buns and let rise again for 30-60 minutes until puffy.

Egg Wash: Preheat oven to 350°F (175°C). Whisk an egg and brush on tops of buns.

Bake: Bake buns for 20-25 minutes or until golden brown and hollow-sounding when tapped.

Cool: Remove buns from oven and cool on a wire rack for about 10 minutes before serving.