Fluffy Make-Ahead Dinner Rolls

Oh, dinner rolls. Is there anything better? I'm not a bread snob. No, no. Anything with a nice carbohydrate base will do just fine for me. Few requirements. Few needs. 
So I couldn't pass up the chance to make my own "straight from the 1950s" dinner rolls when I stumbled across this recipe. 
Well, I almost did when I saw that they took up to 5 hours to make. But ah well, I was struck with the Christmas spirit and made them anyway. And (as you'll see), the 5 hour estimate was way over. I mean, they aren't 30 minute rolls or anything, but don't think you'll be chained to the kitchen for an entire day and a half.
These, like the "impossible breakfast casserole" come from the January 2007 edition of Cook's Country. And they looked so buttery and delicious. Well. You find a way of turning these down. 
But, be warned, dear readers. These rolls are temperamental. Knead too long and you'll end up with dense starchy things. Sure, they'll look fabulous, but they'll sit in your stomach like a lump of lead. Be gentle.
Makes 15 large rolls
Ingredients
3 tbsp. unsalted butter, plus 2 tbsp. for bowl and baking dish
1 1/2 cups whole milk
1/3 cup honey
4 tbsp. vegetable shortening
5- 5 1/2 cups all-purpose flour
1 tbsp rapid-rise or instant yeast
2 tsp salt
1 large egg, plus 1 large egg beaten with 1 tbsp water
Method
Adjust oven rack to middle position and heave oven to 200 degrees F. When oven reaches 200 degrees, shut oven off. Grease a large bowl with 1 tbsp. butter. Line 13 x 9 inch baking dish with foil, leaving overhang on all sides. Grease foil with 1 tbsp. butter.
Place milk, honey, shortening, and remaining 3 tbsp. butter in large measuring cup. Microwave on high power until milk is warm (110 degrees) and butter and shortening begin to melt, 1-2 minutes. Stir well.
Mix 4 1/2 cups flour, yeast, and salt in bowl of standing mixer fitted with dough hook. Turn mixer to low and slowly add milk mixture. After dough comes together, increase speed to medium, add 1 egg, and mi until dough is smooth, about 2 minutes. Add another 1/2 cup flour and knead until dough is  shiny and smooth and comes away from sides of mixing bowl, 6 to 7 minutes. (add up to 1/2 cup more flour if dough is too sticky) Turn dough onto floured surface and knead briefly to form smooth cohesive ball. Transfer dough to buttered bowl and turn to coat. Cover bowl with plastic wrap and place in turned-off oven until dough has doubled in size, 50-60 minutes. 
Punch dough down on floured surface and divide into 3 equal pieces. Roll each piece into thick cylinder and cut each cylinder into 5 equal pieces. Working one piece at a time (keep remaining pieces covered with plastic wrap), form dough pieces into smooth rounds and arrange in a prepared baking dish. Lightly press on dough rounds so that they just touch each other. Cover baking dish with plastic wrap and return to turned-off oven until dough rounds have doubled in size, 50-60 minutes.
Remove dish from oven and heat oven to 375 degrees. Unwrap baking dish and brush rolls with egg-water mixture. Bake until rolls are deep golden brown, 25-27 minutes. Remove from oven and cool on wire racks for 5 minutes. Using handles of foil sling, remove rolls from baking dish and cool on wire rack.  (Note: Ok, here's where the recipe says you should cool these puppies for an hour. Ridiculous. They also say that after this, you should cool for another TWO HOURS! after this. My rolls were room temperature in 15 minutes and delicious. So forget that.)