In a small bowl, combine warm water (110°F / 43°C), sugar and active dry yeast. Stir and let sit 5–10 minutes until foamy. In a large bowl or stand mixer fitted with a dough hook, combine 5 3/4 cups of the flour and kosher salt. Add the foamy yeast mixture and melted butter. Mix on low (or stir by hand) until a shaggy dough forms, then knead 6–8 minutes in the mixer (or 8–10 minutes by hand on a lightly floured surface) until the dough is smooth, slightly tacky, and elastic. If dough is too sticky, add remaining flour 1 tbsp at a time.

First rise

Lightly oil a large bowl with the vegetable oil. Place the dough in the bowl, turn to coat with oil, cover with plastic wrap or a towel, and let rise in a warm draft-free spot until doubled, about 1 to 1 hour 15 minutes.

Divide and shape

Punch down the dough and turn it out onto a lightly floured surface. Divide into 8 equal pieces for large pretzels (or 12 for medium). Roll each piece into a rope about 20–24 inches long for large, or 16–18 inches for medium. Shape each rope into a classic pretzel by forming a U, crossing both ends twice, bringing ends to the base of the U and pressing to seal. Place shaped pretzels on a parchment-lined baking sheet.

Prepare baking soda bath and preheat oven

Preheat oven to 450°F (230°C). In a wide, shallow saucepan, bring 8 cups water and 3/4 cup baking soda to a simmer over medium heat. Reduce heat so it stays at a gentle simmer (do not boil vigorously).

Boil pretzels

One or two at a time (depending on pan size), carefully lower each shaped pretzel into the simmering baking soda bath for 20–30 seconds per side. Use a slotted spatula to flip once so both sides are coated. Remove, drain briefly on the slotted spatula, and return to the parchment-lined sheet.

Egg wash and salt

Whisk the large egg with 1 tsp water. Brush each pretzel lightly with the egg wash, making sure not to pool the egg. Sprinkle coarse sea salt evenly over the pretzels.

Bake

Bake in the preheated 450°F (230°C) oven for 12–15 minutes, rotating the pan halfway through, until deep golden brown. Baking time may vary with size—larger pretzels need the longer time. Remove from oven and transfer to a rack to cool 5 minutes before serving.

Pickled Jalapeño Queso (about 2 cups)

Make roux and milk base

In a medium saucepan over medium heat, melt the unsalted butter. Whisk in 2 tbsp flour and cook for 1–2 minutes, stirring constantly, until the raw flour smell disappears but the roux does not brown. Slowly whisk in 1 1/2 cups whole milk, smoothing lumps and bringing the mixture to a gentle simmer. Cook, whisking, until slightly thickened, about 2–3 minutes.

Add cheeses and seasonings

Reduce heat to low. Add the softened cream cheese and whisk until incorporated. Add the shredded cheddar and monterey jack a handful at a time, whisking until fully melted and smooth between additions. Stir in the chopped pickled jalapeños and 1 tsp pickled jalapeño juice. Season with ground cumin, smoked paprika, 1/2 tsp kosher salt and 1/4 tsp black pepper. Taste and adjust salt or jalapeño juice for brightness or heat.

Finish and garnish

Keep the queso on very low heat or transfer to a small warm serving pot. Stir in chopped cilantro if using. If the sauce becomes too thick, thin with up to 2–4 tbsp additional milk until desired dipping consistency is reached. Keep warm while pretzels bake; stir occasionally to maintain smoothness.