Test your sourdough starter by placing a small spoonful in a glass of water. If it floats to the top, it's ready!
In a large mixing bowl, combine the sourdough starter, milk, oil, egg, and about half of the flour. Stir until smooth. Cover and let sit at room temperature for 30 minutes.
Add the salt and remaining flour and stir until the dough starts to pull away from the sides of the bowl. (You may need more or less flour. You want a slightly sticky dough.)
Cover with plastic wrap or a lid and let sit at room temperature for 30 minutes. Fold one corner of the dough over to the other side. Rotate the bowl a quarter turn and fold over each of the corners.
Repeat 3-5 times. The bread dough will become much more smooth and elastic after it has rested and been stretched a few times. (Tip - if the dough seems too wet, flour your hands before folding & stretching the dough. If it seems too dry, wet your hands with water.)
Form the dough into a ball shape in the bowl and cover with plastic wrap or a lid. Refrigerate for at least 12 hours, but up to 24.
The next day, take the dough out of the fridge and divide it into 12 pieces. Form each piece into a ball and place in a greased 9x13" pan.
Cover the pan with plastic wrap and let the rolls raise in a warm place until doubled. Since the dough is cold, it can take 4-6 hours.
When the rolls have doubled, preheat your oven to 400°. Cut slits in the top of each roll. Spray the top of the rolls with water, then cover with another 9x13" pan. (This traps steam inside and leads to chewier rolls.)
Bake at 400 degrees with the cover on for about 25 minutes. Remove the top pan and bake for another 15-20 more minutes, or until golden brown.
If desired, brush the warm rolls with melted butter.