Make the tangzhong: In a small saucepan, whisk together water, soy milk, and bread flour until no lumps remain. Cook over medium, stirring constantly with a heat-proof spatula, until it thickens to the consistency of wallpaper paste, about 2-3 minutes. Remove from heat and allow to cool until just warm to the touch, about 10 minutes. (Too hot will kill your yeast.)
1/2 cup water, 1/3 cup soy milk, 1/3 cup bread flour
Proof yeast: Add lukewarm soy milk into the bowl of a stand mixer. Whisk in the yeast along with 1/4 teaspoon of your sugar and allow to proof for about 5 minutes, until foamy.
1 cup lukewarm soy milk, 4 ½ teaspoons active dry yeast
Mix the dough: Add the cooled tangzhong, softened butter, bread flour, sugar, and salt to the bowl. Mix on medium speed with the paddle attachment until a shaggy dough forms.
tangzhong, 6 tablespoons stick-style vegan butter, 5 cups bread flour, 1/3 cup granulated sugar, 1 ½ teaspoons fine salt
Knead dough: Switch to the dough hook and knead 6-8 minutes, or until the dough is smooth and elastic. The dough should clear the sides of the bowl and spring back when poked. If it's very wet or sticky, add in more flour 2 tablespoons at a time, mixing fully between additions. (By hand, knead for 8-12 minutes.)
First rise: Shape the kneaded dough into a ball. Lightly oil the bowl, add the dough, and flip it over to coat with oil. Cover and let rise in a warm spot until doubled in volume, about 1 hour (up to 2 hours in a chilly kitchen, or faster in a warm kitchen).
vegetable oil or vegan butter