In a large mixing bowl, combine warm water, sugar, and yeast. Let it sit for about 5 minutes until it becomes frothy.
Add the melted butter, salt, and flour to the yeast mixture. Mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Incorporate the shredded cheddar cheese and chopped jalapeños into the dough, kneading until evenly distributed.
Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat your oven to 450°F and line a baking sheet with parchment paper.
In a large pot, bring 10 cups of water and the baking soda to a boil.
Punch down the risen dough and divide it into 8 equal pieces. Roll each piece into a long rope (about 24 inches) and shape it into a pretzel.
Carefully drop each pretzel into the boiling water for about 30 seconds, then remove and place on the prepared baking sheet.
Brush each pretzel with the beaten egg and sprinkle with coarse sea salt.
Bake for 12-15 minutes or until golden brown. Let cool slightly before serving.