Add the yeast and 1 teaspoon of sugar to the warm (110 degree F) water. Mix and set aside for about 5 minutes or until it becomes frothy.
Meanwhile, in the bowl of a stand mixer fitted with a dough hook, add the flour, salt, and 2 tablespoons of sugar. Add the yeast water and melted butter.
Mix the dough for 5 minutes. The dough should be tacky but not sticky to touch. If it feels sticky, add a bit more flour, 1 tablespoon at a time.
Scoop the dough out onto a lightly floured surface and shape it into a ball. Transfer the dough to a lightly oiled bowl and rotate all around to coat the entire thing in oil. Cover with a towel and leave to rise until doubled in size, about 2 hours.
Once the dough has risen, move one of the oven racks to the middle position and the other rack to 2 spots below it. Line 2 baking sheets with parchment paper.
Preheat the oven to 450 degrees F and begin heating the water in a Dutch oven or large pot over medium-high heat.
Deflate the dough onto a lightly floured surface and cut into 8 roughly equal pieces. Allow the dough to rest for another 10 minutes.
Then, roll one dough ball into a rope until it is about 16 inches long. Use a sharp knife or bench scraper to cut 1-inch sections. Lightly toss the pieces in flour and transfer them to one of the lined baking sheets.
When all of the dough has been cut into 1-inch pieces and the water has come to a gentle boil, pour the baking soda into the water. Then, working in batches, add some of the pretzel dough pieces to the water and boil for 30 seconds. Do not over-boil!
Remove the pieces to the second lined baking sheet and continue until all the dough has been boiled. Spread the pretzel pieces to both lined baking sheets so that there is room between each piece.
Brush each piece with the egg wash. Then sprinkle each one with some of the coarse kosher salt or pretzel salt.
Bake with one baking sheet on each rack in the oven for 8 minutes. Then, rotate the sheets and bake another 7 to 8 minutes or until the pretzel bites are deeply golden brown.