Step 1

Grease a very large bowl with butter. Pour 1½ cups warm water (100°–115°) into the bowl of a stand mixer. Sprinkle yeast over. Add brown sugar and stir to dissolve. Let sit until foamy, 5–7 minutes.

Step 2

Stir in bread flour, beer, kosher salt, and remaining 2 Tbsp. butter with a wooden spoon or spatula until a shaggy dough forms. Mix with dough hook on medium-low speed until dough forms into a smooth ball, about 2 minutes. (You might need to help dough form into a ball by scraping up some flour from bottom of bowl with your hands.) Dough should be firm and might be a little tacky, but not sticky. If dough is still sticky, add flour 1 Tbsp. at a time, mixing until smooth. If dough is too dry, add warm water 1 tsp. at a time. Continue to mix on medium-low speed until dough is smooth and elastic, 5–7 minutes. (Alternatively, mix dough ingredients in a large bowl, then turn out onto a clean work surface and knead by hand, about 10 minutes.)

Step 3

Transfer dough to prepared bowl and cover tightly with plastic wrap. Let rise in a warm place until doubled in volume, about 1½ hours.

Step 4

Place racks in upper and lower thirds of oven; preheat to 500°. Turn out dough onto a clean work surface and punch down to deflate. Divide into 8 equal pieces (if you have a kitchen scale, weigh the dough before cutting, then divide by weight; otherwise, eyeball it). Working with 1 piece at a time and keeping remaining dough covered with a damp kitchen towel, shape dough into a rope about 12" long and ¾" in diameter, applying light pressure with your palms and working from center of dough out to the ends. If you need more friction, lightly spray work surface with water.

Step 5

Cut rope into 8 pieces about 1½" long. Arrange on 2 rimmed baking sheets, spacing ½" apart. Repeat with remaining pieces of dough. Cover with plastic wrap and let rise at room temperature until increased in size by about half, 20–30 minutes.

Step 6

While dough pieces are going through second rise, bring 8 cups water to a boil in a large pot. Carefully add baking soda, which will bubble violently.

Step 7

Using a large spider and working in 2 batches, gently dip dough pieces into boiling solution. Cook, turning, until pieces are fully coated, about 20 seconds. Using spider, remove from liquid and drain on paper towels. Divide between 2 lightly oiled rimmed baking sheets, spacing at least 1" apart.

Step 8

Beat egg with 1 Tbsp. water in a small bowl, then brush dough pieces with egg wash. Sprinkle with toppings. Bake pretzels, rotating sheets from front to back and top to bottom halfway through, until deep brown in color, 8–12 minutes. Let cool slightly.

Step 9

Serve pretzel bites with cheese dip and/or mustard alongside.

Step 10

Do Ahead: Pretzel dough before rises can be made 1 day ahead. Wrap in plastic and chill. Let come to room temperature, then let rise in a warm place until doubled in volume, 3–4 hours.