Warm the milk in the microwave for about 40 seconds.
Pour the milk, sugar and yeast into the bowl of a stand mixer and whisk.
Add in the salt, egg, and vanilla and whisk until combined.
Add the flour and mix with the dough hook for about 1 to 2 minutes on low until combined.
Cut the butter into pieces and add to the mixer. Raise the mixer to 4, or medium, and knead with the dough hook for about 4 minutes. The dough will slap the bowl and look greasy. The butter may pop out. Let the mixer run and it will come together. The dough is done when it no longer sticks to the side of the bowl and is smooth. Cover the dough with plastic wrap and let rise until doubled in size, about 1 to 2 hours.
Once doubled, place the dough on parchment paper and roll into a rectangle or oval as thin as you can.
Spread warmed butter on the dough. Then sprinkle the dough with sugar, brown sugar, and cinnamon.
Roll up the dough starting with the long side. Once rolled, stretch the dough out and form into a 'U'. Take the left side and place it over the right, and take the right side and place it down over the left (see pictures) to form a pretzel shape. Place the pretzel on parchment and then on a baking sheet. Loosely cover with plastic wrap and let it rise for a 2nd time for about 1 - 2 hours.
Once it's puffy, preheat the oven to 350 degrees.Melt 1 T of butter and brush it on top of the pretzel. Bake the pretzel for 20 -25 minutes until golden.
While the pretzel cools, whisk the ingredients for frosting.
Place the cooled pretzel on it's serving dish and pour the frosting over the pretzel.If you like it less sweet, drizzle just a bit of the frosting. If you like it sweet, spread all of the frosting.Enjoy!