In a large mixing bowl with an attached dough hook, combine the beer, brown sugar, and yeast. Stir, then let sit 5-10 minutes until the yeast gets very foamy. Add the flour and knead for 10 minutes until a firm, but slightly tacky, dough forms. If needed, add an additional tablespoon or two of flour to achieve this texture.
Lightly oil a clean bowl. Drop in the dough ball and flip to coat both sides. Cover and let rise until doubled, about an hour.
Line two large baking sheets with parchment paper.
Punch down the dough and divide into 8 balls. Working one ball at a time, press and roll into a roughly 18-20 inch rope. Cross one end towards the center, then fold the opposite end overtop and twist around the first end twice. Attach the two end pieces to the center of the rope to achieve the pretzel shape. See photos for reference. Lay the pretzel onto the prepared baking sheet. Repeat with the remaining dough balls.
Preheat oven to 450 degrees.
Bring about 10 cups of water to a boil in a large pot. Add the baking soda (carefully, it will foam like a sonabitch). Drop 1-2 pretzels at a time into the water and boil for 30 seconds. Remove the pretzels with a slotted spoon, letting excess water drain into the pot, and add back to the baking sheet. Repeat with the remaining pretzels.
Brush each pretzel with the beaten egg and sprinkle generously with pretzel salt. Bake 12-15 minutes until deeply golden.
In a bowl, whisk together the mayonnaise, Dijon and grainy mustards, prepared horseradish, honey, garlic and onion powders, and a pinch of salt. Serve the pretzels warm with the mustard!