German Soft Pretzels with Cheddar Beer Sauce

For the pretzels:

1. In a large bowl, stir the brown sugar into the warm water until dissolved. Sprinkle the yeast over the water and let stand until foamy, about 5 minutes. Stir in the vegetable oil and 3 cups of the flour. Knead in the remaining flour; the dough will be slightly sticky.

2. Transfer the dough to a floured work surface and knead until silky, about 3 minutes. If the dough is very sticky, knead in up to 1/4 cup more flour. Transfer the dough to a large, oiled bowl, cover with plastic wrap and let it stand at room temperature until doubled in bulk, about 45 minutes.

3. Preheat the oven to 450 F. Line 3 large cookie sheets with parchment paper and butter the paper. Punch down the dough and turn it out onto a floured work surface. Knead the dough lightly, flatten it out and cut it into 24 pieces. Roll each piece into a 9-inch stick about 1/2 inch thick. Transfer the sticks to the prepared cookie sheets, leaving at least 2 inches between them. Let them stand uncovered until puffed, about 25 minutes.

4. In a large, deep skillet, stir the baking soda into 2 quarts of water and bring to a simmer over high heat. Reduce the heat to moderate. Using 2 slotted spoons, carefully transfer 6 pretzel sticks at a time to the simmering water and cook for 30 seconds, turning once. Transfer the pretzel sticks to paper towels to drain, then return them to the cookie sheets, spacing them out evenly. Continue cooking until you’ve finished all of the pretzels. You will need to add about 1 cup of hot water before cooking each batch of pretzels.

5. Lightly beat the egg with the tap water in a small bowl. Brush the pretzel sticks with the egg wash and sprinkle with salt. Bake until richly browned, about 10 minutes. Serve warm or at room temperature, with mustard.

For the cheddar beer sauce:

1. In a saucepan over medium heat, melt the butter. Add the flour and cook, stirring constantly, for 2 minutes. Slowly whisk in the milk and beer, increase the heat to medium-high and bring the mixture to a simmer. Add the mustard, Worcestershire and hot sauce and cook, whisking occasionally, until the mixture begins to thicken, 3 to 5 minutes.

2. Working in batches, add the cheese in large handfuls, whisking until each batch has completely melted before adding more. Season with salt and pepper. Serve cheese sauce warm with German soft pretzels.