In a large bowl or stand mixer bowl, add the tangzhong, sourdough discard, eggs, whole milk, white sugar, instant dry yeast, and vanilla. Whisk all the wet ingredients until smooth.
All the tangzhong, 1/2 (120g) cup sourdough discard (100% hydration), 2 large eggs, 1/2 (100g) cup whole milk, 1/4 (50g) cup granulated white sugar, 1 tsp 4g vanilla extract, 2 1/4 (7g) tsp instant dry yeast
Add the flour and salt to the wet ingredients, and transfer to the stand mixer and knead on Speed 1 or knead by hand for about 3-4 minutes until the dough comes together.
3 1/2 (450g) cups all-purpose flour, 1 3/4 (10g) tsp fine sea salt
Once the dough has come together, add the softened butter slowly by the Tablespoon. Once you've mixed in a Tablespoon, add another until all of the butter has been worked into the dough.
Mix the butter into the dough with the stand mixer set to Speed 1, or you can do this by kneading the butter in slowly by hand. The dough should me smooth and slightly sticky.
8 (113g) Tbsp unsalted butter