1cupwater plus 2 tablespoons warm water (125 to 130 degrees)
4 1/2cupsall-purpose flour plus more for rolling
vegetable oilfor the bowl
8cups for water
1/4cup baking soda
1egg white lightly beaten with 1 teaspoon water, for glaze
1tablespoon coarse kosher saltfor sprinkling
Beer Cheese Sauce
8ounces American cheese
To make the pretzel sticks: Proof the yeast by combining it with 2 tablespoons warm water and 1 teaspoon sugar in a small bowl. Once the yeast begins to foam and bubble, it is ready to use. Transfer the yeast mixture to the bowl of a stand mixer and add the flour and salt; and begin to mix, using the dough hook. Slowly stream the remaining 1 cup of warm water into the flour; a ball of dough will form. Continue to mix for another minute to knead the dough. Grease the bowl with vegetable oil, place the dough ball in the bowl, cover with a towel, and let rise for approximately 35 minutes.
The dough should double in size. Four a cutting board and place the dough on the board. Knead and then divide the dough into 16 portions. Roll each portion into a cigar shape and use a sharp knife to cut 2 or 3 slits into the top. Cove with a towel and let rise for another 25 minutes. Preheat the oven to 375 degrees.
On the stovetop, bring the 8 cups of water to boil in a large saucepan. Add the baking soda and the remaining 2 tablespoons of sugar (the water will foam for a moment). Drop 4 pretzel sticks at a time into the boiling water and cook for 30 seconds per side. Use a slotted spoon to remove the sticks and place them on a baking sheet.
Brush the pretzels with the egg white glaze and sprinkle generously with coarse salt. Bake until brown, about 25 minutes. Transfer to a wire rack and let cool for 10 minutes. Serve warm or at room temperature.
Beer Cheese Sauce
Chop the cheese into 1-inch cubes and place in a small saucepan with 4 ounces of beer. Warm and stir over low heat until the cheese has melted