Activate your yeast: Stir together water, yeast and sugar in the bowl of your stand mixer, then let stand for 5-7 minutes. The mixture should be foamy and bubbly.
Add the beer, butter, flour, and salt then knead using the dough hook on low speed until combined. Continue to knead on medium low until your dough is smooth and elastic, 5-7 minutes. The dough should be slightly tacky but not at all sticky. Place dough in a lightly greased large bowl and cover with plastic wrap. Let rise in the fridge for 8-24 hours.
Line two baking sheets with parchment paper and set aside. Turn the dough out on an unfloured work surface. For the next few steps, always keep the dough covered and work with 1 portion at a time.
Punch down to deflate and cut into 8 equal portions. Roll out each portion one at a time into into 12-16 inch long ropes by rolling with light pressure against the work surface with your palms from the center outwards. Keep the center thicker than the ends.
Go back to the first rope of dough and continue to roll each log out into 24-28 inch ropes.
Form the pretzels: position the rope into a U with the ends pointing away from you. Cross the ends over twice starting about three inches from the tips, then bring the ends down towards yourself and press into the U at 4 and 8 o’clock. Place the pretzels on the baking sheet about 1 inch apart, as you form them.
Let rise in a warm spot, until doubled (about 30 minutes) or in the refrigerator (up to 8 hours). Arrange the racks in your oven: one in the upper third and one in the lower third. Preheat to 500°F.
Add about 3 inches of hot tap water to a large pan or pot, then place over high heat to just below a boil. Add the baking soda and stir until dissolved, being careful not to splash it on yourself. Soak each pretzel one at a time into the baking soda water for 20 seconds, using a spoon to carefully spoon the water over the top.
Once each pretzel has been dipped, brush with an egg wash, top with coarse sea salt, and immediately bake until the pretzels are deep mahogany, 8-12 minutes, rotating the pans half way through, front to back, top to bottom. Cool slightly and enjoy!