Method 1 (Autolyse Method - Recommended):
In the bowl of a stand mixer, combine sourdough starter, buttermilk, eggs, sugar, and flour. Mix on low speed until just combined into a shaggy dough.
Cover and let rest for 30 minutes (autolyse).
After 30 minutes, sprinkle the salt and vanilla over the dough. Mix on medium speed for 3-4 minutes.
Add the softened butter one chunk at a time, mixing well between each addition. Continue mixing for 8-10 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl.
Place dough in a lightly greased bowl, cover, and let rise at room temperature (68-72°F) for 8-12 hours, or until doubled in size.
Method 2 (All-at-Once Method):
Combine all ingredients in the bowl of a stand mixer.
Mix on medium speed for 10-12 minutes until smooth and elastic.
Place dough in a lightly greased bowl, cover, and let rise at room temperature for 8-12 hours, or until doubled.