Step 1: Make the Tangzhong
In a small saucepan, whisk together the flour and water until smooth.
Cook over medium-low heat, stirring constantly, until the mixture thickens into a paste (about 2–3 minutes). It should resemble a thick roux. Remove from heat and let cool slightly.
Step 2: Activate the Yeast
In a small bowl, combine the warm milk and 1 teaspoon of the sugar. Sprinkle the yeast over the top and let it sit for 5–10 minutes , until foamy.
Step 3: Mix the Dough
In a large mixing bowl or stand mixer, combine the flour, remaining sugar, salt, tangzhong, yeast mixture, eggs, and softened butter.
Mix on low speed (or by hand) until a shaggy dough forms. Increase the speed to medium and knead for 8–10 minutes , until the dough is smooth, elastic, and slightly tacky but not sticky. Add a little more flour if needed, 1 tablespoon at a time.
Step 4: First Rise
Place the dough in a lightly oiled bowl, turning it to coat all sides. Cover with a clean kitchen towel or plastic wrap.
Let the dough rise in a warm, draft-free area for 1–1.5 hours , or until doubled in size.
Step 5: Shape the Dough
Punch down the dough to release air bubbles. Turn it out onto a lightly floured surface.
Divide the dough into 3 equal portions and shape each into a ball. Roll each ball into an oval, then roll it up tightly like a jelly roll. Place the rolls seam-side down in a greased loaf pan.
Step 6: Second Rise
Cover the shaped dough loosely with a towel or plastic wrap. Let it rise again for 30–45 minutes , or until puffy and nearly doubled in size.
Step 7: Bake
Preheat your oven to 350°F (175°C) . If desired, brush the dough with the egg wash for a shiny crust.
Bake for 25–30 minutes , or until the bread is golden brown and sounds hollow when tapped on the bottom.