Add warm water to bowl of stand mixer. Sprinkle yeast and sugar over the water and gently combine together. Let mixture sit for 10 minutes until it's foaming. If there is no foam, that means the yeast is dead. This could be due to the water being too hot or the yeast being expired.
Add flour and salt to mixture and stir with a dough hook until it forms a ball. If it is too sticky to the touch, add more flour, about 1 tablespoon at a time, until it is manageable. Once manageable, remove dough from bowl and place on floured surface.
Begin to knead by hand for 5 minutes until the dough is soft. You can also do this in the stand mixer but I like kneading by hand so I can tell when the texture is right. When finished, place ball of dough in a large, greased bowl. Cover with damp paper towel and let rise for about an hour, or until doubled in size. Make sure to place in a warm, draft-free spot. I like to place my dough in the microwave.
While the dough is rising you can prep the cheese dip. If you haven't shredded your cheese yet, do it now. Then jump down to the cheese instructions.
Once the dough has risen, punch dough down with your fist. Turn out dough onto floured surface. Cut dough into 8 even wedges. Take one wedge and begin rolling into a log. Gradually increase the length of the log until it's about 12 inches long. Cut log into about 10 pieces. Set pieces aside or on floured sheet pan. Roll and cut remaining wedges.
Prepare water bath for the pretzels. Place 8 cups of waters into a large sauce pan and heat to high. Once water is boiling, add brown sugar and, carefully, add baking soda. Stir to help the sugar and soda dissolve. Once dissolved, reduce heat to medium. Preheat oven to 450 degrees.
Gently add pretzel bites to water. Add as many that will fit without crowding the pan. Boil for 30 seconds and then flip to other side to boil for another 30 seconds. Remove bites and place on baking sheet.
When all bites are done boiling, beat egg with 2 teaspoons of water. Brush mixture over each pretzel. Sprinkle each pretzel with a little coarse sea salt. Bake in preheated oven for 12-15 minutes until golden brown. Let cool for 5 minutes before serving. Serve with beer cheese dip and veggies.