Dissolve the yeast and sugar in 1 cup of warm water. Allow the yeast mixture to sit for five minutes, or until it is frothy on top.
While waiting for the yeast to become frothy, whisk together 2 cups of the flour with 1/2 teaspoon of salt in a large bowl. Once the yeast mixture is frothy, pour it into the bowl with the flour and stir until it forms a shaggy ball of dough.
Turn the dough out onto a lightly floured surface and knead for 8 minutes. Incorporate 3/4 to 1 cup of additional flour while kneading. After kneading for 8 minutes, the dough should be smooth, elastic, and should spring back when poked with a finger. Place the dough in a lightly greased bowl, cover loosely, and let rise for one hour, or until double in volume.
Once the dough has risen, punch it down to deflate. Turn the dough out onto a clean surface, pat the dough down into a round disc, then cut into 16 equal sized wedges. Roll each wedge into a thin 24-inch long rope, then twist into the classic pretzel shape. For pretzel buns, roll the wedges into balls (cut into 8 pieces for larger rolls) and for pretzel bites, cut the ropes into one inch sections. Place the shaped pretzels on a baking sheet covered with parchment paper and coated lightly with non-stick spray. Allow to rise for 30 minutes.
Preheat the oven to 425 degrees. Bring a large pot of water to a rolling boil, then carefully add 1/4 cup of baking soda. Add two or three pretzels to the pot at a time and let boil in the baking soda water for 60 seconds on each side. Let the boiled pretzels drain for a few minutes on a wire rack before transferring back to the parchment lined baking sheets.
Prepare an egg wash by whisking together one egg and one tablespoon of water. Liberally brush the egg wash over the pretzels, then sprinkle with coarse sea salt. Bake the pretzels for 15-18 minutes, or until deep golden brown on the surface.