Pour beer into microwave safe bowl and microwave for 20-30 seconds to make just slightly warm, around 110° F.
Pour warm beer into bowl of stand mixer (or large bowl) and add brown sugar, salt, and yeast. Stir slightly to incorporate. Let sit for 5 minutes until yeast gets foamy.
Add melted butter and flour and knead with dough hook on low until dough ball is formed and smooth, not sticking to sides of bowl.
Turn dough out onto floured surface, then lightly oil bowl and return dough ball back to bowl. Cover with plastic wrap and let rise in a warm area for about 1 hour, or until doubled in size.
After dough has risen, preheat oven to 425° F and line two baking sheets with parchment paper.
In a small bowl, whisk together egg yolks and 2 Tbsp water. Set aside.
In a large pot bring 6 cups of water and baking soda to boil. Reduce heat to simmer.
While waiting for water to boil (ha) turn dough out onto floured surface and divide into 8 pieces. Roll each piece into a rope about 20" long then twist into pretzel shape.
One at a time, place shaped pretzel into simmering baking soda water for 30 seconds. Remove from pot with slotted spoon and place on parchment baking sheet.
Brush each pretzel with egg yolk wash then sprinkle with coarse salt. Place in hot oven and bake at 425° F for 12-14 minutes until golden brown.
Beer Cheese Dip
While pretzels are baking heat butter, cream cheese and milk in small pot to just simmering. Whisk in flour and let simmer for 1 minute to slightly thicken.
A little at a time, add small handfuls of cheese whisking between each to let cheese melt. Whisk in beer and remove from heat.
Serve immediately as dipping sauce for pretzels.
Notes
For the warm environment, I usually turn my oven on 200° F with the door slightly ajar, let it heat up then turn it off. Then I'll place the bowl in the oven with the door still slightly ajar for about 10-15 minutes and then close the oven.