Preheat oven to 400 F. Lightly grease a quarter sheet pan or a 9x13-inch rimmed cookie sheet.
In a small saucepan, melt butter.
When butter is mostly melted, stir in milk, and heat mixture to 100-110 F.
Meanwhile, add yeast and honey to the bowl of a stand mixer fitted with a paddle attachment (or a large mixing bowl if mixing by hand).
When milk mixture is at temperature, add to yeast and honey; stir to combine.
Add salt and egg, and stir until combined.
Stir in 2 cups all-purpose flour.
Add remaining flour 1/4 cup at a time until dough clings to paddle and cleans the sides of the bowl. Dough will still be pretty sticky.
With floured hands, shape dough into 12 rolls, and place dough on prepared baking sheet.
Cover, and let dough rest for 10 minutes in a warm spot.
Bake for 10-12 minutes, or until lightly golden brown.
When rolls are done baking, brush with 2 tablespoons melted butter.
Butter: I like to use salted butter in these rolls. If using unsalted butter, increase the salt in the rolls to 1 teaspoon.
Milk: You can use anything from skim to whole milk. Using whole milk will give you a richer, softer roll.
Milk temperature: It's important that the milk/butter mixture isn't too hot. If you don't have a thermometer, then the mixture should feel like warm bath water. If it's too hot for you, it's too hot for the yeast and can kill the yeast.
Yeast: There are 2 1/4 teaspoons of yeast in a packet. If you are using packets, you will need 3 packets to give you enough for 6 teaspoons (which is the equivalent of 2 tablespoons) of yeast. If you would prefer to use active dry yeast, substitute an equal amount for the instant yeast. After step 5, let the mixture sit for 5-10 minutes, or until foamy. Then, continue with the recipe as written. If the yeast doesn't foam, start over. Otherwise, your rolls won't rise.
Flour: Be sure to only use as much flour as is necessary to give you a sticky dough. Using too much flour will give you heavy, dry, or doughy rolls.
Rising: Since the rising time is so short, it really helps the rolls to rise if they are in a warm spot. If your kitchen isn't warm, simply preheat your cold oven to 350F for exactly 60 seconds. Turn the oven off, and you now have a great spot for your rolls to rise.
Brushing the rolls: If you want a stronger honey flavor to the rolls, add a tablespoon of additional honey to the butter and brush the rolls with honey butter after baking.