For the Pretzels:

In a large bowl, combine the water, sugar, and kosher salt and sprinkle the yeast on top.
Let the mixture sit for 5-10 minutes, or until the yeast is foamy.
Add the flour and melted butter and stir until the dough comes together.
Knead the dough on a lightly floured surface for 5-7 minutes, or until smooth and elastic.
Grease a large bowl with vegetable oil and place the dough inside.
Cover the bowl with plastic wrap and let the dough rise in a warm place for 1 hour, or until it has doubled in size.
Preheat the oven to 450°F.
In a large pot, bring the water and baking soda to a rolling boil.
Divide the dough into 12 equal pieces.
Roll each piece into a long rope and form into a pretzel shape.
Working in batches, boil the pretzels in the water for 30 seconds on each side.
Remove the pretzels from the water with a slotted spoon and place them on a greased baking sheet.
Brush the pretzels with the beaten egg yolk and sprinkle with coarse sea salt.
Bake the pretzels for 12-14 minutes, or until golden brown and crispy.

For the Honey Mustard Sauce:

In a small bowl, whisk together the Dijon mustard, honey, apple cider vinegar, and garlic powder until well combined.

Serve the pretzels warm with the honey mustard sauce on the side.