To a large measuring cup, add water, milk, and butter. Cover with a paper towel or wax paper. Warm in the microwave for 60 seconds then stir until the butter is fully melted. Check the temperature and return to the microwave and heat in 15 second increments until temperature reaches 100-110ºF. Do not exceed 110º. The butter may not look melted at first. If the temp is 100-110ºF, it will melt if you keep stirring. Resist heating more to melt the butter as this will cause the temperature to be too high to keep the yeast alive and active
¾ cup water, ½ cup milk , 4 tablespoons unsalted butter
Add the sugar and sprinkle in the yeast. Stir or whisk to combine and set aside.
¼ cup granulated sugar, 4 ½ teaspoons instant yeast
In a large bowl, add 3 ½ cups of flour and salt. Stir or whisk to combine.
3 ½ - 4 cups all-purpose flour, 1 teaspoon salt
Make a well in the center of the flour and add lightly whisked egg and pour in milk/yeast mixture. Use a wooden spoon to stir the ingredients until they come together in a shaggy dough.
1 large egg
Generously flour a work surface and dump dough out onto it. Turn dough over to coat both sides in flour. Knead gently a few times until all the loose bits of flour come together in a ball and you have a somewhat smooth ball. If the dough is very sticky, sprinkle some of the reserved ½ cup of flour, a tablespoon at a time, onto the dough and knead in until a smooth dough forms that isn’t overly sticky. You may not use all the flour.
Cover the dough with a clean towel and allow to rest while you prepare the baking dish, about 10 minutes. This is technically the first rise, even though you will see very little to no increase in volume of the bread dough.
Melt the remaining 4 tablespoons of butter in a microwave safe bowl or Pyrex measuring cup. Be sure to cover the top with a paper towel or wax paper to prevent the butter from exploding all over your microwave. Once melted, use a pastry brush to butter the bottom and sides of a 9x13 inch baking dish. Set aside the buttered pan and the remaining melted butter.
4 tablespoons butter
Remove towel from the dough. Press dough gently into a square about 1 inch thick. Cut into 5 rows of 3 to make 15 (or 3 rows of 4 to make 12 slightly larger rolls). If using a scale, the total dough should weigh about 1000 grams and each piece should weigh 66-67g, if making 15.
Pick up one piece of dough at a time to shape into a ball. Fold in the corners to gather them together, pinching to seal. Turn dough ball so it is right side up and cup your hand around it, circling your hand around the dough to form a smooth ball. Place shaped dough balls into the prepared pan in 5 rows of 3 (or 4 rows of 3). Dough balls may be touching.
Cover with the clean towel and let rise for 20 minutes. Dough will rise just a bit. Meanwhile, preheat the oven to 375°F.
Brush tops of dough gently with melted butter. Sprinkle with flaky salt, if desired. Bake rolls in the preheated oven for 18-20 minutes.
Once the tops of the rolls are browned (internal bread temp = 200°F), remove from the oven and immediately brush liberally with melted butter.