Sweet Fluffy Milk Bread

1. In a small saucepan, combine 3 tablespoons of bread flour, 1/2 cup of water, and 1/2 cup of whole milk.
2. Cook over medium heat, whisking constantly until the mixture thickens to a pudding-like consistency.
3. Remove from heat and let it cool to room temperature.

Preparing the Dough

1. In a large mixing bowl, combine 2 1/2 cups of bread flour, 3 tablespoons of sugar, 2 teaspoons of instant yeast, and 1 teaspoon of salt.
2. Add the cooled tangzhong, 1/2 cup of warmed milk, and 1 large egg to the dry ingredients.
3. Mix until a shaggy dough forms.
4. Add 1/4 cup of softened unsalted butter and knead the dough by hand or with a stand mixer for about 10-15 minutes, until the dough is smooth and elastic.
5. Place the dough in a lightly greased bowl, cover it with a damp cloth, and let it rise in a warm place for about 1-2 hours, or until it has doubled in size.

Shaping and Baking the Bread

1. Once the dough has risen, punch it down to release the air.
2. Divide the dough into 4 equal parts.
3. Roll each part into a ball, then roll each ball into an oval shape.
4. Fold the oval in thirds, then roll it out again into a rectangle.
5. Starting from the short end, roll the rectangle into a tight roll.
6. Place the rolled dough pieces seam side down into a greased loaf pan.
7. Cover with a damp cloth and let it rise again for about 1 hour, or until doubled in size.

Preparing the Egg Wash and Baking

1. Preheat your oven to 350°F (175°C).
2. In a small bowl, whisk together 1 large egg and 1 tablespoon of milk to make the egg wash.
3. Brush the egg wash over the top of the risen dough.
4. Bake for 30-35 minutes, or until the top is golden brown and the bread sounds hollow when tapped.
5. Remove from the oven and let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely.