In a mixing bowl, combine warm water, yeast, and sugar. Let sit until foamy, about 5 minutes.
Add the flour, salt, and butter. Mix with the dough hook until dough forms. Cover with a towel and let rise in a warm place for 1 hour or until doubled.
Lightly flour a clean work surface. Punch down the dough and set it on the floured surface.
Divide the dough into 16 equal pieces. Form the dough into smooth balls by pinching the dough at one side, until smooth.
Line a large baking sheet with parchment paper. Place the dough balls on the baking sheet, spaced at least 1” apart. Cover with a towel and let rise in a warm place for about 30 minutes.
While the rolls rise, heat 2 tablespoons butter in a small saucepan over medium heat. Whisk in the flour. Cook for 1 minute, stirring frequently.
Pour in the beer and whisk until smooth. Add the cheese in small amounts, stirring until melted and smooth.
Preheat the oven to 425°F.
Bring 2 quarts of water to a low boil. Add the baking soda and lower the heat to a simmer.
Place the rolls into the water and boil for 30 seconds, turn over and continue cooking for 30 seconds. Remove with a slotted spoon and arrange them on a baking sheet. Brush the rolls with the egg wash. Sprinkle with salt.
Bake for 18-20 minutes, until the pretzels are golden and cooked through. Garnish the cheese with chives and serve hot.