Activate the Yeast: In a large mixing bowl, combine the warm water, yeast, and sugar. Stir gently and let it sit for about 5 minutes until the mixture becomes frothy, indicating that the yeast is active.

Make the Dough: Add the salt and 2 cups of flour to the yeast mixture, stirring until combined. Gradually add more flour, 1/2 cup at a time, until the dough comes together and is no longer sticky. Knead in the minced jalapeños and shredded cheddar cheese until evenly distributed throughout the dough. Continue to knead on a floured surface for about 5-7 minutes until the dough is smooth and elastic. You may not need all the flour; use just enough to achieve a workable dough consistency.

Let the Dough Rise: Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm place for about 1 hour or until it has doubled in size.

Prepare the Pretzel Bath: While the dough is rising, preheat your oven to 450°F (230°C) and line two baking sheets with parchment paper. In a large bowl, carefully combine the hot water and baking soda, stirring until the baking soda dissolves. Set aside.

Shape the Pretzel Twists: Once the dough has risen, punch it down and divide it into 8 equal pieces. Fold the rope in half, then twist the two strands together to form a twist shape. Place each twist onto the prepared baking sheets.

Dip in Baking Soda Bath: Carefully dip each pretzel twist into the baking soda solution for about 10-15 seconds, making sure it is fully submerged. This step helps give the pretzels their characteristic color and texture. Remove with a slotted spoon and place back on the parchment-lined baking sheets.

Egg Wash and Topping: Brush each pretzel twist with the egg wash and sprinkle generously with coarse salt.

Bake: Bake in the preheated oven for 10-12 minutes, or until the pretzels are golden brown and the cheese is bubbling and slightly crisp.

Finish with Butter: Remove from the oven and brush each pretzel twist with melted butter. Let them cool slightly before serving.