In a small saucepan, combine 1/4 cup bread flour, 3 tbsp water, and 3 tbsp milk over medium heat.
Whisk constantly until it thickens into a paste. Remove from heat and let it cool to room temp.
In a large bowl, combine bread flour, sugar, salt, and instant yeast.
Add the cooled flour paste, milk, and egg. Mix to form a shaggy dough.
Knead the dough until it becomes smooth and elastic. This takes about 10–15 minutes.
Add the softened butter and knead until fully incorporated and dough is smooth again.
Cover and let it rise in a warm place until doubled in size, about 1 to 1.5 hours.
Punch down the dough and divide into 3 equal parts. Shape each into a ball.
Roll out each ball into an oval, fold the sides inward, and roll up tightly.
Place each rolled piece into a greased loaf pan. Cover and let rise again for 45–60 minutes.
Preheat oven to 350°F (175°C).
Brush the top with milk or egg wash if desired. Bake for 30–35 minutes until golden brown.
Remove from oven and let cool in the pan for 10 minutes, then transfer to wire rack to cool completely.