Mix flour, sourdough starter, lukewarm water, powdered milk, melted butter, brown sugar, yeast, and salt in a stand mixer with a dough hook. Knead until smooth and elastic (about 5 minutes). Add water if dough is dry.

Form the dough into a ball, grease a bowl, place the dough in it, cover, and let rise at room temperature for 1 hour.

Turn dough out onto a lightly greased surface. Shape into a rectangle, divide into 12 pieces, and cover with plastic wrap.

Roll each piece into an 18-inch rope and twist into a pretzel shape. Place on a baking sheet.

Preheat the oven to 450°F (230°C).

Prepare a water bath by boiling water, reducing heat, then dissolving baking soda. Boil each pretzel for 30 seconds and place back on the baking sheet.

Brush pretzels with egg wash (egg beaten with water), then sprinkle with coarse sea salt.

Bake pretzels in the oven until dark golden brown (12-15 minutes).