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 ½ cups of flour.
Add remaining flour until dough clings to paddle and cleans the sides of the bowl. It's important to only add enough flour to get the dough to just clear the side of the bowl.
Switch to the dough hook, and knead for 2 minutes (or by hand for about 5 minutes).
While dough is kneading, stir together granulated sugar and cinnamon in a wide, shallow dish.
Add melted butter to a separate shallow dish. Set cinnamon sugar dish and melted butter dishes aside.
Preheat oven to 400F. Line a 9x13-inch rimmed cookie sheet with parchment paper or a silicone baking liner. Set aside.
Divide dough into 12 pieces.
Roll piece of dough into rope 8 inches long.
Dip in butter, and then roll in cinnamon-sugar mixture.
Tie dough into knots, and place dough on prepared baking sheet. If you'd like to see more about shaping the knots, check out the video just above the recipe.
Repeat process with remaining dough.
Cover, and let dough rest for 10 minutes.
Bake for about 9-12 minutes, or until lightly golden brown.
While the knots are baking, prepare the icing.
Stir together melted butter, powdered sugar, and vanilla.
Add 1 tablespoon milk, and stir in. Continue adding milk until icing reaches desired consistency. I use about 1 1/2-2 tablespoons for a thicker icing.
Remove knots from oven, and let cool for 5-10 minutes.
Drizzle icing over knots, and serve warm.
Video
Notes
Yeast: If you would prefer to use active dry yeast, substitute an equal amount for the instant yeast. Let the mixture sit for 5-10 minutes, or until foamy. Then, continue with the recipe as written.
Flour: Be sure that your flour isn't packed when you measure it. I stir mine first to make sure that I'm not getting too much flour. Too much flour can make the knots heavy or dry.
Dipping: I've tried forming a knot and then dipping in butter and sugar. The knots didn't work nearly as well that way.