Make the tangzhong. Add the flour and water to a saucepan. Cook over medium heat, stirring, until it becomes a thick gel. Let it cool completely.
Mix the dough. In a stand mixer, add the eggs, sugar, salt, cooled tangzhong, flour, and starter. Mix everything except the butter until just combined. Rest for 20 to 30 minutes.
Knead the dough for 5 minutes. Then add the butter a little at a time, kneading until it is fully mixed in and the dough is smooth.
Proof at room temperature for 2 to 2.5 hours. If you like, do one set of stretch and folds after the first hour.
Cover and refrigerate overnight, 8 to 16 hours.
The next day, divide the dough into 8 pieces, about 133 g each. Grease the loaf pan with butter or line it with parchment paper.
Shape each piece into a ball (boule): flatten slightly, fold the edges into the center, flip seam side down, and roll in small circles to make a tight, smooth ball. Place the balls in the pan.
Let the dough proof until doubled in size, about 5 to 6 hours depending on room temperature.
Preheat the oven to 180°C (350°F). Brush the dough with egg wash.
Bake for 30 to 40 minutes, until deep golden.
Cool before slicing.