Make Tangzhong: Combine 4 tbsp whole milk, 2 tbsp water, and 2 tbsp bread flour in a saucepot. Whisk, heat over medium, whisk until thickened.
Mix yeast with 1/2 cup warm milk, let sit for 8 minutes.
In a stand mixer bowl, combine 2 1/2 cups bread flour, 2 1/2 tbsp sugar, and 1 tsp salt. Mix.
Add milk-yeast mixture to flour, then Tangzhong paste, whole egg, and egg yolk. Mix until incorporated.
Gradually add softened butter, knead for 5-8 minutes.
Let dough rise for 1-1.5 hours until doubled.
Divide dough into 6 pieces, shape into balls, let rise for 1-2 hours.
Brush with egg wash, bake at 375°F (190°C) for 16-18 minutes.
Brush with melted butter after baking. Cool on a wire rack before using for burgers.
Your donation to Vidcook can help us continue to provide our free and valuable service as it costs a decent money to run! You can donate via PayPal by pressing the button below.