Step 1: Make the Tangzhong

• In a small saucepan, whisk together the milk, bread flour, and water.
  
• Cook over medium heat while whisking constantly until the mixture thickens into a smooth paste, about 2–4 minutes.
• Remove from heat and allow to cool slightly.

Step 2: Activate the Yeast

• In a small bowl, combine the warm milk, sugar, and active dry yeast.
• Stir gently and let sit for 5–10 minutes until foamy.
  

Step 3: Make the Dough

• In a large mixing bowl or stand mixer bowl, combine the bread flour, sugar, and salt.
• Add the yeast mixture and mix on low speed.
• Add the cooled tangzhong paste, whole egg, and egg yolk.
• Mix until a rough dough forms.
• Slowly drizzle in the oil while kneading until the dough becomes smooth, soft, and slightly tacky.

Kneading Times

Stand mixer: 8–10 minutes

By hand: 10–12 minutes

Step 4: First Rise

• Lightly grease a large bowl with oil spray or butter.
• Place the dough into the bowl and cover.
• Let rise in a warm place for about 1 hour or until doubled in size.
  

Step 5: Shape the Buns

• Turn the dough onto a lightly floured surface and gently deflate it.
• Divide into 6 equal portions (about 108g each if weighing).
• Shape each piece into a tight ball by pulling the edges inward and rolling gently.
• Place onto a parchment-lined baking sheet, leaving room for expansion.
  

Step 6: Second Rise

• Cover loosely with a towel or lightly greased plastic wrap.
• Let rise for 1½–2 hours until puffy and nearly doubled in size.
  

Step 7: Bake

• Preheat oven to 375°F.
• Brush the tops gently with beaten egg wash.
• Bake for 15–18 minutes, or until deeply golden brown.

Step 8: Final Touch

• Immediately brush the warm buns with melted butter for a glossy, soft finish.
  
• Let cool for at least 1 hour before slicing.