Prepare the yeast. In the bowl of a stand mixer with the hook attachment on, stir together 1 1/2 cups of warm water, sugar, and yeast until blended, then let it sit for 5 minutes.
Blend the ingredients. Add about 3 1/2 cups of flour, the salt, and melted butter to the bowl. Mix on low with the hook attachment until well blended. Add more flour as needed for the dough to come together. Raise the speed to medium, and continue kneading for 4 to 6 minutes or until dough is smooth and elastic.
Let the dough rise. Grease a large bowl with the oil, add the dough, turn it to coat, cover with the plastic wrap and place in a warm, draft-free place to double in size, about 1 hour.
Preheat the oven to 450 degrees F. Generously grease 2 baking sheets or line with parchment paper.
Prepare the water bath. In a medium saucepan over high heat, add the 8 cups of water and baking soda. Bring to a boil, and stir to blend.
Form the pretzel sticks. While waiting for the water to boil, place the risen dough on a lightly floured surface. Divide the dough in half, then divide each half into 12 balls, for a total of 24 balls. Roll out each ball into a rope 4 to 5 inches long. Dust off any excess flour from the pretzels.
Put the pretzels in the water bath. Gently lower each pretzel into the boiling water, 2 or 3 at a time, and cook for 20 to 30 seconds. Remove the pretzels with a large slotted spoon or spatula, gently shaking off any excess water, then place the pretzels on the baking sheets. Mix the egg yolk with a little water to think in a small bowl. With a pastry brush, lightly brush the egg yolk on top of the pretzels, then sprinkle with the pretzel or coarse salt.
Bake the pretzels. Bake for 12 to 17 minutes, or until dark golden brown. Cool slightly, then transfer the pretzels to a wire rack to finish cooling before serving.
Make the honey mustard dip. In a small bowl, mix together the mayonnaise, honey, and mustard, and serve alongside the pretzels.
SNAPPY TIPS: Be careful not to overcook the pretzels in the water bath.SNAPPY SUBSTITUTIONS: Instead of the honey mustard dip, serve the pretzel sticks with your favorite chip dip or cheese dip.