Add the milk to a large bowl. Add the starter and whisk to combine, then whisk in the eggs until well mixed. Place the butter into the bowl and stir to combine. The butter will be in small pieces.
Add the bread flour and all purpose flour, sugar, and salt to the bowl. Use a wooden spoon or spatula to mix, making sure to incorporate all of the flour, until a shaggy dough has formed.
Cover the dough with a tea towel, and, every 20 minutes for the next hour, do three rounds of stretches and folds.
Day One: Bulk Fermentation
Place a lightly damp tea towel and a large plate over your bowl, then set aside to rise at room temperature overnight or for about 8 hours. The dough should double in size during this time.
If your home temperature is quite warm, this will likely take less than 8 hours. See notes below.
Day Two: Shaping the Rolls
Refrigerate the risen dough for at least 2 hours before shaping if possible. The cold dough is much easier to shape.
Lightly flour a clean surface and turn the proofed dough out onto it.
Separate the dough into 16 equal pieces.
Grease a large baking dish with butter and set aside.
Take each piece of dough and repeat the stretching and folding motion from earlier.
Lightly coat one side of the piece in flour, then gently stretch one edge and fold it in to the middle of the piece. Rotate, repeating the motion, until a ball has formed.
Place the ball onto a clean surface and use your hand to rotate the ball counterclockwise. This will help the roll to form a skin on the outer layer so that it keeps a nice shape when rising and baking.
Repeat this until all of the rolls are shaped, placing each roll into the baking dish as you go.
Day Two: Second Proof
Cover the rolls with a tea towel and set them aside to rise at room temperature for 2-3 hours, or until almost doubled in size. If you want to extend the fermentation time even longer, you could refrigerate the shaped rolls overnight again.
If refrigerating, the buns must prove at room temperature first. Refrigerate after they have risen. The cold buns can then be baked directly from the refrigerator.
Day Two: Baking
Preheat the oven to 350°F (180°C), then place the rolls into the oven.
Bake for 25-30 minutes, or until very golden brown.
Remove from the oven and brush the tops with a generous amount of melted butter. This both softened the rolls and adds even more flavour.
Cool for at least 10 minutes before serving. The rolls will keep well for a few days in a sealed container at room temperature and freeze well.