Place the beer in a microwave-safe bowl and heat for about 45 seconds. You want the beer to be a little over 100 degrees, but less than 115.
In the bowl of your stand mixer, place the sugar and the salt, then pour the warm beer over top. (FYI you don't need a stand mixer to make this, you could easily do it by hand, but it's just more work). Sprinkle the yeast over the beer, and leave it to bloom for about 5 minutes.
Once the yeast has bloomed, stir in the melted butter, then place the bowl on the mixer, fitted with a dough hook. Turn the mixer on its lowest speed, and slowly add in the flour, until it is all incorporated.
Allow the dough to mix for another 5 minutes or so, until it is no longer sticky and it comes away from the side of the bowl and clumps up on the dough hook.
Pull the bowl off of your stand mixer and clean off the dough hook, pulling the dough into a cohesive ball. Slather a little vegetable oil on the ball so it doesn't stick, place it back in the bowl, and cover with a towel. Place in a warm spot and allow to rise for an hour. It should at least double in size.
Dump the dough out onto your work surface, and punch it down. Roll it out into a log and cut it into 8 sections. Roll each section out into a long, skinny rope, a foot long. Fold the rope in half, and wrap it around itself, then pinch the ends together to make a pretzel stick. You can also, of course, make pretzel shapes, as well.
Bring a large pot of water to a boil, and add a few tablespoons of baking soda. Drop the pretzels, two at a time, into the boiling water, and cook for 30 seconds. Pull them out using a slotted spoon or a spider, and place them on silpat- or parchment-lined baking sheets.
Brush the pretzels with the aquafaba/oil mixture, then generously sprinkle them with coarse salt.
Bake pretzels in a preheated 425 oven for about 20 minutes, or until nicely golden.
Remove from oven and enjoy hot with your favourite mustard to dip.