In the bowl of a stand mixer, combine the milk, melted butter, sugar, egg, salt, and starter.
Attach the dough hook and mix on low speed. Gradually add the flour until a soft, pliable dough forms. Scraping down the sides of the bowl as needed. *see note.
Increase to medium speed and knead for about 15 minutes, or until the dough is smooth, silky, and pulls away from the sides of the bowl, but is still tacky.
Cover the bowl with plastic wrap and let rise at room temperature until almost doubled, about 6 hours.
Once the dough has nearly doubled, refrigerate it for at least 1 hour (and up to 12 hours). This step makes the dough easier to handle when shaping.
When ready to shape, generously butter or oil a 12-cup muffin tin to prevent sticking.
Divide the chilled dough into 24 equal pieces (the full dough should weigh about 975 g, making each piece about 40 g).
Shape each portion into a tight ball and place two dough balls in each muffin cup—they should fit snugly.
Cover the rolls loosely with oiled plastic wrap and let them rise again until doubled.
Once risen, preheat your oven to 350°F.
Bake for 11–18 minutes, or until the rolls are golden brown and reach an internal temperature of 190°F.
Baste with butter immediately once removed from the oven. Serve warm.
Notes
Don't add all of the flour at once, add it gradually, stopping when dough is still a bit sticky to avoid dense rolls.