Combine warm water, yeast, and sugar in a large bowl and let sit until foamy, about 5 minutes.
Stir in flour, salt, and melted butter until a dough forms.
Knead dough for 5 to 7 minutes until smooth and elastic, then cover and let rise for 45 minutes or until doubled.
Cook ground beef and onion in a skillet over medium heat until beef is browned and onions are soft.
Add garlic powder, Worcestershire sauce, salt, and pepper; stir and remove from heat, letting cool slightly.
Mix shredded cheese into the beef mixture.
Preheat oven to 425 °F and line a baking sheet with parchment.
Punch down dough and divide into 12 to 16 equal pieces.
Flatten each piece into a circle and place 1 to 2 tablespoons of the beef and cheese filling in the center.
Fold edges up and pinch tightly to seal each dough ball.
Bring water and baking soda to a boil in a large pot.
Boil each sealed dough ball for about 30 seconds per side, then remove with a slotted spoon.
Place boiled pretzel bombs on the baking sheet, brush with egg wash, and sprinkle with coarse salt.
Bake for 12 to 15 minutes until deep golden brown.
Let cool slightly before serving warm with mustard, ketchup, or cheesy dipping sauce.