In the bowl of a stand mixer fitted with the dough hook, combine the active starter, warm milk, flour, eggs, salt, sugar, and vanilla extract.
Mix on low speed until a shaggy dough forms.
With the mixer running, add the softened butter one tablespoon at a time, allowing each addition to fully incorporate before adding more.
Scrape down the sides of the bowl as needed.
Increase the mixer speed to medium-high and knead for 7–10 minutes, or until the dough becomes smooth, elastic, and begins pulling away from the sides of the bowl.
Note: Brioche dough is naturally soft, wet, and sticky. Avoid adding extra flour for the softest texture.