Soft Milk-and-Butter Tangzhong Sourdough Batard

Steps

1. Day 1, about 8 a.m.: feed your starter equal weights of starter, flour and water from your own starter supply (not from the recipe's ingredients) and leave it at about 75°F (24°C); it should double and peak in 4 to 6 hours, domed and full of bubbles.
2. While the starter rises, make the tangzhong: in a small pot, whisk 25 g of the flour into the milk until smooth. Cook over medium-low heat, stirring constantly, for 2 to 4 minutes until it thickens to a pudding-like paste. Scrape into a large bowl and cool to room temperature, about 30 minutes.
3. When the starter peaks, add the starter, water and sugar to the cooled tangzhong and whisk until loose. Add the remaining 475 g of flour and mix until no dry flour remains. Cover and rest 30 minutes.
4. Sprinkle the salt over the dough and squeeze it in, then work in the 20 g of softened butter a little at a time, kneading in the bowl for 5 to 8 minutes until the dough is smooth and supple. This dough is about 65% hydration (counting the water in the milk and starter) and about 1.8% salt.
5. Bulk rise, covered, at about 75°F (24°C) for 4 to 5 hours. During the first 2 hours, do 4 sets of stretch-and-folds 30 minutes apart, wet hands lifting and folding each side of the dough over itself. Bulk is done when the dough has grown about 75%, looks domed and airy, and jiggles when the bowl is shaken.
6. Turn the dough onto a lightly floured counter, pat into a rectangle, roll up tightly from the short side into a batard, and pinch the seam closed. Place seam side down on a parchment-lined baking sheet.
7. Cover loosely and cold-proof overnight in the fridge, 10 to 14 hours.
8. Day 2: take the loaf out and let it warm at about 75°F (24°C) for 1 to 2 hours, until it looks puffy and springs back slowly when poked. Meanwhile, preheat the oven to 375°F (190°C).
9. Make one shallow slash down the length of the loaf. Bake 35 to 40 minutes, until deep golden and the center reads 190°F (88°C), since this dough is enriched with milk and butter. Tent with foil if it browns too fast.
10. Right out of the oven, brush the crust all over with the 10 g of melted butter to keep it soft.
11. Cool the loaf on a rack for at least 2 hours before cutting into 12 slices.