In the bowl of a stand mixer or large bowl, combine tangzhong, sweet levain, eggs, milk, vanilla, salt and sugar.
All of the tangzhong, 3/4 cup (200g) sweet levain, 2 (100g) large eggs, 1/3 cup (80g) warm milk, ¼ cup (50g) granulated sugar, 1¾ tsp (10g) salt, 1 tsp vanilla
Add flour and mix with a dough hook on low or use a dough whisk until a shaggy dough forms.
3 1/2 cups (450g) all-purpose flour
With the mixer on medium-low, add butter a tablespoon at a time, letting each piece incorporate before adding the next. Alternatively if mixing this dough by hand, knead one tablespoon of butter into the dough at a time.
10 T (142g) unsalted butter, softened
Knead for 10–15 minutes, or until smooth, elastic, and slightly tacky. The dough should pass the windowpane test. If using a stand mixer, I suggest using your hand to scrape the dough down and knead for a minute after 8 minutes to make sure ingredients are incorporated, then complete remaining kneading time on low. Do not cut your kneading time short.
Place in a greased bowl, cover, and bulk ferment at warm room temp for 5-6 hours.
Perform 1 stretch and fold after 30 minutes if using stand mixer. If you mixed this dough by hand perform 3 sets of stretch and folds at 30 minute intervals during the first 2 hours. Dough should rise about 90-100%. At this point you can continue to shape rolls, or you can cover your dough and refrigerate overnight for cold fermentation.