Step 1: Make the Tangzhong

1. In a small saucepan, whisk together the 20g of bread flour and 100g of water until no lumps remain.

2. Place the saucepan over medium-low heat. Cook, whisking constantly, until the mixture thickens into a smooth, thick paste, similar to pudding. You should see lines forming on the bottom of the pan as you whisk. This will take about 2-3 minutes.

3. Immediately transfer the Tangzhong to a small bowl, cover it with plastic wrap touching the surface to prevent a skin from forming, and let it cool to room temperature. You can place it in the fridge to speed this up.

Step 2: Make and Knead the Milk Bread Dough

1. Combine Dry Ingredients: In the bowl of a stand mixer fitted with a dough hook, combine the 350g of bread flour, 55g of sugar, 5g of yeast, 5g of salt, and 20g of milk powder. Briefly mix to combine.

2. Add Wet Ingredients: Add the beaten egg, lukewarm milk, and the cooled Tangzhong to the dry ingredients.

3. Knead (Part 1): Mix on low speed until a shaggy dough forms. Increase the speed to medium and knead for about 5-7 minutes, until the dough comes together and looks smooth.

4. Add the Butter: Add the 40g of softened butter, one tablespoon at a time, waiting until each piece is incorporated before adding the next. The dough may look greasy and separated at first—this is normal. Keep kneading.

5. Knead (Part 2): Continue to knead on medium speed for another 10-15 minutes, until the dough is very smooth, elastic, and pulls away from the sides of the bowl.

6. The Windowpane Test: To check if it’s ready, take a small piece of dough and gently stretch it between your fingers. It should stretch thin enough to be translucent without tearing. This indicates proper gluten development.

Step 3: The First Proof

1. Form the dough into a smooth ball. Place it in a lightly greased bowl, cover it with plastic wrap or a damp towel, and let it rise in a warm, draft-free place for 60-90 minutes, or until it has doubled in size.

Step 4: Prepare the Crispy Topping

1. Combine Dry Ingredients: While the dough is proofing, make the topping. In a medium bowl, whisk together the 115g of all-purpose flour, 60g of sugar, baking soda, baking powder, and salt.

2. Cut in the Butter: Add the cold, cubed butter to the flour mixture. Use your fingertips or a pastry cutter to quickly rub the butter into the flour until the mixture resembles coarse, sandy crumbs.

3. Add Wet Ingredients: In a small separate bowl, whisk together the egg yolk and milk. Pour this into the flour-butter mixture.

4. Form the Dough: Use a spatula or your hands to gently and quickly bring the mixture together into a soft dough. Do not overwork it.

5. Chill: Wrap the topping dough in plastic wrap and chill it in the refrigerator for at least 30 minutes.

Step 5: Shape the Buns and the Topping

1. Divide the Bread Dough: Once the dough has doubled, gently punch it down to release the air. Transfer it to a lightly floured surface and divide it into 12 equal pieces (each should be about 55-60g).

2. Shape the Buns: Roll each piece of dough into a smooth, tight ball. Place the balls on a large baking sheet lined with parchment paper, leaving a few inches of space between them.

3. Shape the Topping: Remove the chilled topping dough from the fridge and divide it into 12 equal pieces. Roll each piece into a ball. Place one ball of topping between two sheets of parchment paper and gently press or roll it into a thin, flat circle, just large enough to cover the top and most of the sides of a bread bun.

4. Apply the Topping: Carefully peel the topping circle off the parchment and drape it over one of the dough balls, gently pressing it onto the surface. Repeat for all 12 buns.

Step 6: The Second Proof

1. Cover the assembled buns loosely with plastic wrap and let them rise in a warm place for another 30-45 minutes, or until they are puffy and have increased in size by about 50%.

Step 7: Final Touches and Baking

1. Preheat Oven: While the buns are proofing, preheat your oven to 375°F (190°C).

2. Apply Egg Wash: Gently brush the exposed sides of the bread dough only with the prepared egg wash. Try to avoid getting egg wash on the cookie topping, as this will give you a better visual contrast after baking.

3. Score the Topping (Optional but Recommended): For the classic look, use a bench scraper or the back of a knife to gently press a crosshatch (diamond) pattern into the cookie topping. Be careful not to cut all the way through to the bread.

4. Bake: Place the baking sheet in the preheated oven and bake for 15-18 minutes, or until the buns are a deep golden brown and the topping is crisp and golden.

5. Cool: Let the buns cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely. They are best enjoyed warm.