1. In a large mixing bowl, stir together the warm water, granulated sugar, and active dry yeast. Let the mixture sit for 5 minutes until it becomes foamy.

2. Add the all-purpose flour, salt, and softened butter to the bowl. Mix until a dough forms, then knead for about 5 to 7 minutes until smooth and elastic.

3. Place the dough in a lightly greased bowl, cover it, and let it rise for 1 hour or until doubled in size.

4. Preheat the oven to 425°F and line a baking sheet with parchment paper.

5. Bring the 9 cups of water to a gentle boil in a large pot, then carefully stir in the baking soda.

6. Punch down the dough and divide it into 6 equal portions. Roll each portion into a rope, then cut into bite sized pieces.

7. Drop the dough pieces into the baking soda bath in small batches for about 20 to 30 seconds, then lift them out with a slotted spoon and place them on the prepared baking sheet.

8. Whisk together the egg yolk and 1 tablespoon water, then brush the tops of the pretzel bites with the mixture.

9. Sprinkle the pretzel bites with coarse pretzel salt.

10. Bake for 12 to 15 minutes, or until deep golden brown.

11. Remove from the oven and immediately brush with melted butter.

12. Serve warm with cheese sauce, mustard, or your favorite dip.