In the bowl of a stand mixer, add: sourdough starter, water, brown sugar, flour, salt, softened butter.

Using the dough hook attachment, knead on medium to medium-high speed for 7–10 minutes, until the dough becomes smooth and elastic.

Lightly grease a medium bowl with olive oil and place the dough inside. Cover with greased plastic wrap or a damp towel.

Let rise at room temperature for 3–6 hours, or until the dough has at least risen 50% or up to nearly doubled in size.

Transfer the covered dough to the refrigerator and let it ferment for 8–24 hours.

Line a baking sheet with parchment paper and cut 8 small parchment squares.

Remove dough from the fridge and divide into 8 equal portions (about 100–110 g each).

Roll the dough into a rope about 20–24 inches long, form a 'U' shape, cross the ends over each other and twist twice, then fold the twisted ends down and gently press onto the base.

Place each shaped pretzel onto its own parchment square.

Cover loosely with greased plastic wrap and let rise for about 1 hour, or until slightly puffy.

Preheat your oven to 220°C (425°F).

In a large pot, combine water, baking soda, and brown sugar. Bring to a gentle boil over medium-high heat.

Carefully lift each pretzel by the parchment square and gently lower it into the water. Boil each pretzel for 30–40 seconds per side.

Place boiled pretzels onto a parchment-lined baking sheet.

In a small bowl, whisk the egg and brush each pretzel generously with egg wash, then sprinkle with coarse salt.

Bake at 220°C (425°F) for 15–20 minutes, or until deeply golden brown.

Let pretzels cool slightly before serving.