In the bowl of a stand mixer, combine warm water and sugar. Sprinkle yeast on top and allow it to sit for 1 minute. Next add in salt and melted butter. Stir until just combined. Add in 3 3/4 cups of flour, one cup at a time, mixing with dough hook attachment for stand mixer. Dough should pull away from sides within 4 -5 minutes. If it is still sticky, add 1/4 at a time until dough bounces back if touched.
Take dough out of bowl, clean the bowl if it's needed and coat it with oil. Return dough to the bowl and cover with a clean tea towel or plastic wrap. Place in a warm area for around 30 minutes or until dough has doubled in size.
Preheat oven to 425 degrees and line two baking sheets with parchment thats been lightly sprayed with cooking spray.
In an 8 quart sauce pan, bring 10 cups of water and baking soda to a boil.
Put dough onto a flat, floured surface and divide into 8 equal pieces. Roll each piece into a long rope of about 15-20 inches. With a sharp knife, cut the dough into one inch pieces. Optional- Using scissors, you can cut a small "x" in each pretzel bite.
Place around 8-10 pretzel bites into the boiling water and let boil for about 10 seconds. Set a timer to keep from overcooking. Remove pretzel bites from the water and place onto the prepared baking sheets. Be mindful that the pieces are not touching. Brush each pretzel bite with the egg wash. Sprinkle with coarse salt.
Bake for 10-12 minutes or until golden brown. Let pretzel bites cool for around 5 minutes before eating. Serve with Beer Cheese Dip.