Preheat your oven to 450°F (232°C) and line a large baking sheet with parchment paper. This will prevent the pretzels from sticking and ensure even baking.

In the bowl of a stand mixer fitted with the dough hook, combine 1 1/4 cups warm water, 2 1/2 teaspoons active dry yeast, and 1 tablespoon granulated sugar. Allow the mixture to stand for 5-10 minutes, or until it becomes frothy. Stir in 1/2 teaspoon salt. Add 3 cups of all-purpose flour and mix until combined. Then, mix in the minced jalapenos and shredded cheddar cheese. Gradually add more flour, a little at a time, until the dough forms a cohesive ball that is slightly tacky but not sticky. You may not need all 4 cups of flour.

Fill a large bowl with 4 cups very hot water. Stir in 1/4 cup baking soda until dissolved—this creates an alkaline bath that helps give the pretzels their classic flavor and color. In a separate small bowl, whisk together 1 large egg with 2 tablespoons water to make an egg wash; set aside.

On a lightly floured countertop, divide the prepared dough from Step 2 into four equal sections. Roll each section into a log and cut each log into three pieces, resulting in 12 equal pieces of dough. Roll each segment into a rope about 18-24 inches long, then fold each rope in half and twist the two segments together. Pinch the ends and tuck them underneath to form a pretzel twist. Transfer the twists to the prepared baking sheet.

Gently transfer each pretzel twist into the hot baking soda bath from Step 3 for about 30 seconds. Remove using a slotted spoon and return each twist to the baking sheet, re-twisting as needed to maintain shape. Brush each pretzel with the egg wash from Step 3 and sprinkle with coarse salt. I like to add extra coarse salt for more flavor and crunch.

Bake the topped pretzel twists in the preheated oven for 8-10 minutes, or until they are golden brown. Allow them to cool slightly on the baking sheet, then brush the warm pretzels with melted butter for a beautiful sheen and rich flavor. For an extra touch, I let the pretzels cool for just a couple of minutes before brushing on the butter; it really helps the butter soak in.