In a large mixing bowl, combine the warm water, sugar, and yeast. Allow it to sit for about 5 minutes until frothy.
Add the flour and salt to the yeast mixture, stirring until well combined. Knead the dough on a floured surface for about 5 minutes, or until smooth and elastic.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm spot for about 1 hour, or until doubled in size.
Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper.
In a large pot, bring about 10 cups of water to a boil and add the baking soda carefully.
Punch down the risen dough and divide it into small pieces (about 1 inch each). Roll each piece into a ball.
Drop the pretzel bites into the boiling baking soda solution, cooking them for about 30 seconds. Remove with a slotted spoon and place them onto the prepared baking sheet.
Brush each pretzel bite with beaten egg, then sprinkle with garlic powder, grated Parmesan cheese, and coarse sea salt.
Bake in the preheated oven for 12-15 minutes, or until golden brown.
Remove from the oven and immediately brush with melted butter for extra flavor.