Mix the beer and ½ cup water together and heat to 100-110 degrees or the temperature listed on the yeast package. In a mixing bowl, pour in the warm beer and water mixture with sugar and salt. Sprinkle the yeast on top and let it sit until it turns foamy, about five to 10 minutes.
If using a stand mixer, add the flour and ¼ cup melted butter to the beer and yeast mixture and use the paddle attachment on low speed to combine into a shaggy dough. Replace the paddle attachment with the dough hook. Turn the speed up one notch to speed two and knead until smooth and elastic. This should take about four minutes. If kneading by hand, stir in the flour and butter with the beer and yeast mixture in the mixing bowl until it becomes a dough. Turn onto a lightly floured surface and knead until smooth and elastic.
Remove the dough from the bowl, lightly oil the bowl, place the dough back in the bowl and tightly cover with plastic wrap. Allow to sit in a warm place for about an hour or until the dough doubles in size.
Heat the oven to 450 degrees and boil 10 cups water with baking soda.
Meanwhile, divide the dough into eight equal pieces and lightly oil the countertop. Roll the dough under the palm of your hand until it resembles a snake, about 18 inches long. Shape the dough into a U and then cross each end to the opposite side just off center.
One at a time, drop the shaped pretzel into the boiling water and baking soda for 30 seconds. Move to a parchment paper-lined baking sheet. Beat an egg yolk with 1 tablespoon water and brush it over the boiled pretzels. Sprinkle with salt.
Bake until the pretzels turn golden, about 12 to 14 minutes. Remove from oven and lightly brush with remaining 4 tablespoons of melted butter if desired. If the butter brushes off any salt, you can always add more if you'd like.