Place all ingredients but the butter into your bread machine pan in the order listed. Select the DOUGH cycle.
After about a minute or two, open the lid and add softened butter 1 tablespoon at a time.
10-15 minutes into the DOUGH cycle, lift the lid and check your dough again. It should barely stick to the sides and then pull away cleanly. If too wet, add additional flour 1 tablespoon at a time. If too dry, add additional water or milk one tablespoon at a time.
When the dough cycle finishes, the dough should be doubled in size. If not, leave the dough in the bread machine a few more minutes until it you can punch two fingers into the dough and it fills in gradually. If it doesn’t fill in, it has risen too much. If the dough bounces right back and the dough fills in immediately, then it needs to proof (rise) a little bit longer. (This may happen if your kitchen is cold.)
Pull dough out of the machine and onto a floured surface. Knead the dough and form it into one large ball. Divide in half, making 2 balls. Divide each of those balls into 8 equally-sized lumps.
Make a ball from each piece of dough by pulling the dough toward the bottom while turning the dough. (See video.)
Arrange balls in 2 well-greased 8 or 9-inch round or square pans (non-stick is better) and cover with a tea towel or a cheap shower cap. Place in a warm spot until doubled. (I put mine in the microwave where I have already boiled a cup of water for 5 minutes to make it warm and steamy.)
Preheat oven to 350˚F.
Bake in the oven until golden brown, usually about 12-15 minutes. Rotate to get even browning. Internal temperature should reach 190˚F.
Within 5-10 minutes, dump baked rolls out of the pan and let cool on a rack or paper plate so they won’t get soggy from the steam they produce.