In a small jar, combine the flour, water, sugar, and active sourdough-starter. Mix well until no dry flour remains.

Cover loosely and let ripen overnight at room temperature (70-76°F), about 10-12 hours.

The levain is ready when it has doubled, looks bubbly throughout, and smells mildly sweet and tangy. It should dome slightly on top, not collapse.

In a small saucepan, whisk together the flour and milk until smooth.

Cook over medium-low heat, stirring constantly, until the mixture thickens into a paste (like mashed potatoes), about 3-5 minutes. It should reach approximately 150°F (65°C).

Spread onto a plate to cool quickly. Press plastic wrap directly on the surface to prevent a skin. Let cool to room temperature before using.

Cut the butter into ½-inch pieces and set out to soften.

In the bowl of a stand-mixer fitted with the paddle attachment, combine: bread flour, warm milk, beaten egg, sugar, salt, all of the ripe sweet levain, and all of the cooled tangzhong.

Mix on low speed (Stir on a KitchenAid) for 1-2 minutes until everything comes together and no dry flour remains.

Switch to the dough hook. Mix on medium speed (setting 2-3) for 4-5 minutes until the dough smooths out and starts clinging to the hook. It will still stick to the bottom of the bowl. That's okay.

Let the dough rest in the bowl for 10 minutes.

Resume mixing on low speed for 2-3 minutes until the dough gains more strength.

With the mixer running on low, add the softened butter one piece at a time. Wait for each piece to mostly incorporate before adding the next. This takes 5-8 minutes total.

The finished dough will be very soft and slightly sticky. It won't fully clear the sides of the bowl. That's normal for this enriched dough.

Transfer to a lightly greased container for bulk-fermentation.

First set of stretch-and-fold (30 minutes in): With wet hands, stretch one side of the dough up and fold it over to the opposite side. Rotate the bowl 90° and repeat. Do this 4 times total, going around the bowl. The dough will feel loose and extensible.

Second set (1 hour in): Turn the dough out onto a clean counter. Perform a few gentle slap-and-fold until the dough tightens and smooths. Shape into a ball and return to the container.

Let the dough rest undisturbed for the remaining 2½ hours.

Cover the pan with a large plastic bag or damp towel.

Let the dough rise at room temperature (74-78°F) until it reaches about 1 inch above the rim of the pan.

Gently brush the top with milk or egg wash.

Bake uncovered for 30-40 minutes until the top is deep golden brown and internal temperature reaches 190-195°F (88-91°C).

If the top browns too quickly, tent with foil for the last 10 minutes.

If using a Pullman pan with a lid, slide the lid on. No egg wash needed.

Bake for 35-45 minutes until internal temperature reaches 190-195°F (88-91°C).

The loaf sounds hollow when tapped.