Vegan Milk Bread

Mix tangzhong: In a small pan, stir together 2 tablespoons bread flour and 1/2 cup water to remove any lumps.
Cook tangzhong: Heat mixture over medium-high heat, stirring constantly, until it thickens to a paste consistency. (A flexible rubber spatula works well for this.) Remove from heat and allow to cool while you prepare other ingredients.

Proof yeast: In the bowl of a stand mixer, add lukewarm soy milk. Whisk in the active dry yeast and allow to proof for about 5 minutes, or until foamy.
Mix dough: Add the sugar, salt, cooled tangzhong, bread flour, and softened butter. Mix on medium speed with the paddle attachment to bring everything together into a shaggy dough. (If working by hand, use a wooden spoon or spatula to mix the ingredients together.)
Knead with a stand mixer (recommended): Switch to the dough hook attachment and knead on medium speed for 8-10 minutes, until the dough goes from shaggy to smooth and elastic. If the dough seems overly soft or tacky, sprinkle in extra flour 2 tablespoons at a time as needed. Make sure the flour has fully incorporated before adding more.
To knead by hand: Turn the dough out onto a lightly-floured surface and knead by hand for 10-12 minutes, until dough is smooth and elastic. Sprinkle on extra flour as needed if the dough is sticking excessively to your hands or your work surface — but avoid working in too much flour. A bench scraper is also useful to scrape up any dough sticking to your work surface.

Transfer to oiled bowl: Shape the dough into a ball and transfer it to a lightly-greased bowl. Turn the dough ball to coat it with oil. Cover it with a damp kitchen towel, plastic wrap, or a plate to keep it from drying out.
Rise till doubled: Let the dough rise in a warm spot for about 1 hour, or until doubled in volume. It can process slower if it is very chilly in your kitchen — up to 1.5 hours. Go by volume rather than time.

Mix together 1 tablespoon sugar and 1 tablespoon soy milk in a small, microwave-safe bowl or measuring cup. Microwave in 10-15 second bursts until the mixture begins to bubble and the sugar dissolves. Give this a stir. Cover loosely and set aside to cool.

Prep: Lightly grease a standard loaf tin. (9x5” works best, though it can also be made in an 8x4").
Divide dough: Punch down the risen dough and turn it out onto a clean work surface. Divide the dough into 3 parts of roughly equal size. (You can use a digital scale for precision.)
Shape and relax dough: Shape each piece of dough into a ball, then cover and allow to rest for about 10 minutes. This will give the gluten a moment to relax. (You can cover with the same damp towel or piece of plastic wrap used earlier. Or you can simply turn the bowl upside-down to cover the dough balls.)
Roll the dough pieces: With a rolling pin, roll each ball of dough out into a wide oval shape about 1/2” thick. Fold both edges in toward the center, with one edge overlapping the other. Then with the rolling pin, roll gently to widen the dough slightly and roll the piece back to roughly 1/2” thickness. Starting at the edge closest to you, tightly roll the dough into a log. Repeat with the remaining 2 pieces of dough. (Consult the procedure photos for reference.)
Final rise: Pinch the seams gently to seal the dough logs. Then transfer them into the greased loaf tin, evenly spaced, with the seam sides down. Lightly cover the loaf tin and allow to rise in a warm spot for about 1 hour, or until the dough is just cresting over the top edge of the loaf tin. Again — the exact time will vary depending on the temperature of your room.

Preheat oven: Near the end of the rising time, preheat oven to 350°F.
Wash: Lightly brush the top of the loaf with the vegan egg wash mixture prepared earlier. Try to brush it on as evenly as possible so the loaf browns evenly.
Bake: Bake for 30-35 minutes, or until golden brown. The internal temperature should read between 190°F and 200°F to ensure doneness. (If it appears to be browning too quickly, loosely tent it with a sheet of aluminum foil.)
Cool: Allow the loaf to cool in the tin for about 10 minutes before lifting it out and transferring it to a wire cooling rack. The interior of the loaf is still cooking once it comes out of the oven, so I recommend allowing it to cool fully before slicing — otherwise you risk a gummy texture.