First, prepare the pretzels. Preheat oven to 500F, and line two baking sheets with parchment.
Lightly flour your work surface, and divide the dough into 8 equal portions. Roll each portion into a long and skinny log {make it longer than you think you need}, and twist into the traditional pretzel shape. Repeat with all.
Mix the 5 tablespoon of baking powder with water in a large pot, and bring to a boil. Cook each pretzel for about 30 seconds, flipping halfway, then remove and place on prepared baking sheet.
Brush the pretzels with the melted butter, sprinkle with coarse salt, and bake for 10-12 minutes, until golden brown and crisp.
While the pretzels cook, make the beer cheese. In a medium nonstick pot, melt the butter, then whisk in the flour all at once and cook for a couple of minutes, until it smells lightly toasted.
Slowly pour in the milk, followed by the beer, whisking constantly to prevent lumps.
Stir in the cheese until just melted, then remove from heat and add the seasonings.
Serve pretzels and beer cheese warm!