Yes, another roll

Here's yet another roll in my recipe repertoire that I love to make. It's a softer roll, bordering almost on being a brioche, but the dough is much easier to handle. These rolls make great sandwiches, but if done in half the size, really makes a great dinner roll for all those holiday feasts coming up. I use the KichenAid to make these up, so you will start with the paddle attachment, but later switch to the dough hook.
In the bowl, add:
1 large egg
1/2 cup sugar
1 tsp. salt
Mix to blend well. In a 2-cup glass measuring cup, add:
1/2 cup whole (or 2%) milk. (I buy milk that I'm using for baking, since we drink non-fat, in 8-ounce cartons that store on the shelf)
4 T. unsalted butter
Microwave for 25 seconds and check to see if the butter has melted. If not, do 20 seconds more. Add warm water to the measuring cup to bring it up to 2 cups of liquid.
While the mixer is running, pour the milk/butter/water mixture over the above ingredients. Then add: 2 T. dry yeast and mix just until incorporated. Let this sit for 5 to 10 minutes. The mixture should be frothy if your yeast is good; if not start over! Next, add 1 cup Bread flour while the mixer is running and incorporate well. You will do this two more times (for a total of 3 cups of flour). Change to the dough hook and add 2 to 2 1/2 more cups of flour, one cup at a time, until dough comes away from the sides of the bowl. Turn dough out on a very lightly floured board. Meantime, heat 1 T butter in a large glass bowl in the microwave for 40 seconds. Take bowl out and brush sides with the melted butter. Knead the dough until it's smooth, then, place it right-side down into the bowl. Turn it right-side up (you'll see the top has been coated with the melted butter). Place plastic wrap over the opening, making sure it pulls tightly to make a seal. Let dough rise for 40 to 45 minutes. Punch down risen dough and divide into 12 pieces (or if making dinner size rolls, 24 pieces). Roll and flatten each piece and place on a baking sheet that has been brushed with melted butter. When you've done all the rolls, brush the tops with melted butter and place a piece of plastic wrap overtop. You do not have to stretch it tightly because you will next place a cotton dish towel over the pan to protect from drafts. While the rolls are rising a second time, preheat over to 375F-degrees. Let rise, about 20 minutes, then uncover and place in the over. Bake 15 minutes. These rolls have a lot of flavor and really make good sandwiches! Enjoy!