In a small saucepan, whisk together the flour and milk until no lumps remain.

Place over medium-low heat and cook, stirring constantly with a whisk or spatula, until the mixture thickens to a paste-like consistency (similar to thick pudding). This takes 3-5 minutes.

Transfer to a small bowl, press plastic wrap directly onto the surface to prevent a skin from forming, and let cool to room temperature.

In a large bowl (or the bowl of a stand-mixer), combine the bread flour, sugar, salt, and instant-yeast. Stir to distribute.

Add the cooled tangzhong, egg, and warm milk. Mix on low speed for 2 minutes until a shaggy dough forms and no dry flour remains.

Increase to medium speed and knead for 6-8 minutes. The dough will look rough at first, then smooth out. It should pull away from the sides of the bowl but still stick to the bottom.

With the mixer running on low, add the softened butter one piece at a time. Wait until each piece is mostly incorporated before adding the next. This takes about 3-4 minutes.

Once all butter is added, increase to medium speed and knead for another 5-7 minutes. The dough is ready when it's smooth, slightly tacky (not sticky), and passes the windowpane-test.

Shape the dough into a ball and place in a lightly greased bowl. Cover with plastic wrap or a damp towel.

Let rise at room temperature (75-78°F) until doubled in size, about 1 to 1½ hours. The dough should look puffy and feel light when you lift the bowl.

Grease a 9x5-inch loaf-pan with butter or neutral oil.

Gently deflate the dough and turn it out onto a lightly floured surface. Divide into 3 equal pieces (about 190g each if using a kitchen-scale).

Working with one piece at a time, flatten into a rough rectangle about 4x6 inches. Fold the short ends toward the center like a letter, then roll up tightly from the short end into a log. Place seam-side down in the prepared pan.

Repeat with remaining pieces, arranging them side by side in the pan so they touch.

Cover the pan loosely with plastic wrap or a clean kitchen towel.

Let rise until the dough reaches about 1 inch above the rim of the pan, approximately 45 minutes to 1 hour. The dough should look puffy and jiggly when you gently shake the pan.

Divide the dough into 3 equal pieces (about 190g each). Shape them into balls, cover, and bench rest for 15 minutes.

Flatten one piece into a 4x6-inch rectangle. Fold short ends toward center like a letter.

Roll up tightly from short end into a log.

Place seam-side down in greased pan. Repeat with remaining pieces, arranging side by side.

Roll entire dough into a large rectangle (about 9x12 inches).

Roll up tightly from the short end. Place seam-side down in greased pan.

About 20 minutes before baking, preheat your oven to 350°F (175°C) with a rack in the lower third.

Gently brush the top of the dough with milk or melted butter.

Bake for 30-35 minutes, until the top is deep golden brown and the internal temperature reaches 190-195°F (88-91°C).

If the top browns too quickly, tent loosely with foil for the last 10 minutes.

Preheat oven to 350°F (175°C).

Let dough rise until it reaches about ½ inch below the lid.

Slide the lid closed and bake for 35-40 minutes, until the internal temperature reaches 190-195°F (88-91°C).

Remove lid for last 5 minutes if you want a golden top.