Tangzhong (roux starter)

Cup of Yum
1. In a small pot, combine the flour, milk, and water. Over low heat, whisk until smooth and continue stirring until the whisk leaves a clear, thick track at the bottom of the pot.
2. Remove the roux from the heat and scrape it into a glass measuring cup to stop the cooking. If you are not using it right away, cover the starter with plastic wrap, pressing down the wrap onto the surface of the roux to prevent a skin from forming and let cool.

Dough

1. In the bowl of a mixer, use the paddle to combine the flour, sugar, and yeast and mix on low speed briefly. Add the salt and mix for about 10 seconds.
2. Add the egg and the starter. Mix on low speed. When the dough starts to come together, switch to the dough hook. (If the dough doesn't come together, add an additional tablespoon of milk at a time).
3. Increase the speed to medium and add the butter, one or two small cubes at a time. It should take a few minutes to finish adding the butter. Knead for about five to seven minutes more, adding flour as necessary if the dough sticks to the bottom of the mixer. At the end of kneading, the dough should be soft and tacky but not sticky.
4. Shape the dough into a boule, cover the bowl with plastic wrap, and let it rise in a warm place until doubled in size, about one and a half to two hours.
5. Lightly grease two 9 inch round cake pans.
6. Divide the dough in half, and place one half into a bowl and cover it with plastic.
7. Divide the remaining dough into eighths, and roll each portion into a ball (see the link below and in the main post for how to shape dinner rolls). Place the bread rolls in one cake pan so they are equally spaced and not touching. Repeat with the second half of the dough and second cake pan.
8. Cover the cake pans with plastic wrap, and let the dough rise again in a warm, draft-free location until doubled in size, about 2 hours.
9. Thirty minutes before baking, preheat the oven to 350°F.
10. Brush with a tablespoon of melted butter, if you like, then bake for about 18 to 20 minutes until lightly browned and the internal temperature is 190°F.
11. Serve warm or at room temperature.