Grease a large bowl. In the bowl of a stand mixer fitted with a paddle, combine the warm buttermilk and yeast on low speed, and let sit until the yeast has dissolved, about 5 minutes. Add the eggs, granulated sugar, salt, and vanilla, and mix until well combined.
Add the flour, mixing on low speed until incorporated, 1 to 2 minutes. Add the butter, one piece at a time. When all the butter has been added, increase the speed to medium and beat the butter into the dough, until all the little butter pieces are incorporated, about 1 minute. Transfer the dough to the prepared bowl. The dough will be sticky.
Cover the bowl with plastic wrap and let the dough rise for 30 minutes. Remove the plastic wrap and place your fingers or a spatula underneath the dough to gently pull the dough up and fold it over itself. Give the bowl a quarter turn and fold the dough over again. Repeat six to eight more times, until all the dough has been folded over on itself. Cover the bowl with plastic wrap and let the dough rise for 30 minutes. Repeat this series of folding the dough three more times, every 30 minutes, for a rise time of 2 hours.
Tightly cover the bowl with plastic wrap and refrigerate overnight or up to 3 days.