Combine water, milk, butter, sugar, salt, and yeast in the bowl of your stand mixer. Stir and let rest for about 5 minutes, until the yeast becomes foamy.
Add 2 ½ cups of flour and stir on low speed with the dough hook until dough begins to form. Add additional flour, spoonfuls at a time, until a ball of dough begins to form. Knead on medium speed for 4-5 minutes, until a smooth, tacky dough forms, adding flour as necessary. The dough should clear the sides of the bowl and should barely scrape the bottom of the bowl.
Place the dough in an oiled bowl and cover with plastic wrap. Let the dough rest for about 20 minutes, until the dough is puffy.
Turn dough onto an oiled or plastic-lined surface. Pat into a 4x12 inch rectangle. Cut down the center lengthwise, then cut into 6 to create 12 pieces of dough. (My pizza cutter worked well here.) Shape each piece of dough into a ball. Place dough balls into two greased 8-inch or 9-inch round cake pans. (8-inch work better, but 9-inch are fine too.) Cover with plastic wrap.
If you will bake the rolls later, let the dough proof for 10 minutes, then place into zipper bags and store in the freezer. Thaw overnight in the fridge before baking.
If you will bake the rolls now, let the dough proof for 20-25 minutes. They will grow appreciably.
Bake at 350F for 20-25 minutes, until rolls are a light golden color and register at least 190F on the inside. Brush with melted butter if desired. Serve warm.