Mix the warm water, brown sugar, and active dry yeast in the bowl of a stand mixer. Let the mixture sit until it's foamy, about 5-10 minutes.

Add the melted and cooled butter, all purpose flour, and salt. Use a dough hook to mix the dough until it's shaggy. Continue adding more flour 30 grams (1/4 cup) at a time until the dough is smooth and slightly tacky but not sticky.

Knead the dough on medium speed for 6-7 minutes until it's smooth and pulls away from the sides of the bowl. To test if the dough is properly kneaded, give it a firm poke with your finger. If it springs back slowly, it's ready to go. If it springs back right away, knead it for another 1-2 minutes.

Lightly coat a large bowl with neutral oil or cooking spray. Shape the kneaded dough into a ball and place it in the oiled bowl, making sure to coat the ball of dough in oil so it doesn't dry out. Cover the bowl with a tea towel and place in a warm spot. Let the dough rise until it's doubled in size, about 40-45 minutes.

While the dough is rising, combine the 2 liters (8 cups) of water and baking soda in a Dutch oven or large pot. Bring the water to a rolling boil. Preheat the oven to 450°F (230°C). Line two thick sheet pans with parchment paper. Then, whisk the egg with 15 milliliters (1 tablespoon) of water to make an egg wash.

Once the dough has doubled in size, tip it onto a very lightly floured surface. Use a bench scraper to cut it into 16 equal portions, about 65 grams each (but it doesn't have to be perfect). Working one at a time, roll each piece of dough into an even, 18-inch rope. Make a U-shape with the rope. Twist the ends of the rope twice, and then fold the twist over, pressing the ends into the bottom of the U. Place the shaped pretzels on a parchment-lined sheet pan (or another clean surface) and cover them with a linen. Repeat with the remaining dough until you have 16 mini pretzels.

Use a slotted spoon to drop 3-4 pretzels into the boiling water. Boil for 30 seconds, gently pressing the pretzels into the water so they get fully coated. Use the slotted spoon to remove the pretzels, letting as much excess water drip off as possible. Place the boiled pretzels on the prepared parchment-lined sheet pans, and repeat with the remaining pretzels.

With a pastry brush, brush the tops of the pretzels with the egg wash. Sprinkle the pretzels evenly with pretzel salt or coarse salt, to taste. Bake for 12-15 minutes, flipping the pan halfway through, until they are deep golden-brown. Serve the pretzels immediately with beer cheese and mustard. Enjoy!