Warm the 50 grams of water to about 105F, which should feel like comfortable bath water on the inside of your wrist, then whisk in the yeast along with a pinch of sugar taken from the 36 grams and set it aside for ten minutes. Doing this first means that if your yeast is dead you find out at a cost of a few tablespoons of water rather than after committing an entire loaf of ingredients.
While the yeast blooms, whisk the 25 grams of bread flour into the 125 grams of milk for the tangzhong until completely smooth, then microwave in 20 to 30 second bursts, whisking between each one, until it thickens to about the consistency of pudding.
Let the tangzhong rest about 5-7 minutes. It only needs to be warm rather than hot, and because the yeast is blooming separately there is nothing here that requires a thermometer.
Check that the yeast has foamed. If there is no foam after ten minutes, rinse the cup and start over with fresh yeast rather than continuing.
Add the cold milk, the cold water, and the sugar directly to the tangzhong in the same bowl and whisk until smooth, which brings the temperature of the paste down before anything heat sensitive goes in.
Whisk in the egg, then scrape in the bloomed yeast along with all of its liquid, then the melted butter.
Add the flour and salt and mix with a dough whisk just until there are no dry pockets left. The dough will look shaggy, sticky and unpromising at this stage, which is exactly right.
Cover and rest for 30 minutes to let the flour hydrate fully before you do any work on it.
Perform a set of stretch and folds by reaching under one side of the dough, lifting it, folding it over onto itself, then turning the bowl and repeating until you have gone all the way around. See the shaping video for more information.
Cover and rest 30 minutes, then repeat for a total of three sets. If the dough still feels loose and unstructured after the third set, add a fourth and make it a gentle one.
Let the dough rise until it has grown by about 70 percent, which usually takes another hour and a half and puts total bulk fermentation around three hours from mixing. Watch the rise rather than the clock, and check every 30 minutes toward the end because fermentation accelerates as it goes.
Turn the dough out onto an unfloured counter, pre shape it into a loose round, and let it rest 15-20 minutes so the gluten relaxes enough to shape without fighting you.
Shape the loaf by placing both hands underneath on opposite sides, folding those two sides up and together while pushing and squeezing, and pinching the seam closed along the top. Then roll the whole thing up like a sleeping bag, rolling back toward yourself and keeping the tension consistent, and seal the final seam well so no air is trapped inside.
Place seam side down and pull toward you to make the top taunt.
Line a long rectangular food storage container with a cotton cloth held in place with a rubber band around the lip, flour the cloth lightly, and set the loaf in seam side up.
Refrigerate covered for 3 to 4 hours. The dough finishes the last of its proof while it cools, and then it firms up enough to transfer cleanly and take a deep score.
Preheat the oven to 450F. Both loaf pans go in cold, straight off the shelf, so there is nothing to preheat alongside it.
Line one loaf pan with parchment, then use the parchment as a sling to lift the cold loaf out of the basket and lower it into the pan without touching the dough. Invert the second loaf pan on top as a lid.
Bake for 10 minutes with the lid on, which traps the loaf's own steam and keeps the surface soft while the bread is still expanding.
Remove the lid, score straight down the center going deep and confident, then put the lid back on.
Drop the temperature down to 375 degrees F and bake another 25 minutes.
Remove the lid and bake uncovered for 12 to 15 minutes until the internal temperature reaches 195F. Let temperature rather than the clock decide this stage, and watch it closely because the crust takes color quickly here.
Turn the loaf out of the pan, wait a minute or two, then brush on a small amount of softened butter. Butter is what keeps the crust soft, and going heavy with it causes more problems than it solves.
Cool completely on a rack, uncovered and with no towel over it, before slicing. A tangzhong crumb needs to cool fully for the starch to set, and slicing it warm will make a perfectly good loaf look gummy.