In the bowl of a stand mixer fitted with the dough hook attachment, add the yeast, brown sugar, and water and stir together. Let the yeast activate for 10 to 15 minutes until the mixture appears foamy.
Whisk the milk and sourdough discard into the yeast mixture.
Add the bread flour and salt and knead on low until no dry traces of flour remain. (If you are not using a mixer, just use your hands to knead together).
Knead until a cohesive pretzel dough forms, about 3 minutes.
Knead the butter into the dough 1 tablespoon at a time. The dough will initially feel greasy and get progressively smooth and less sticky as the butter is absorbed. This may take a few minutes. (If you’re using your mixer, then it’s easier to finish this by hand). Form into a smooth ball and transfer the dough to a mixing bowl and cover the dough and let it rest for 20 minutes. Preheat the oven to 420°F and line a baking sheet (18 by 13 inches) with parchment paper.
Preheat the oven to 420°F and line a baking sheet (18 by 13 inches) with parchment paper.
Knead the dough for 5 to 10 minutes, try your best to get the dough to appear as smooth as possible, or your pretzel buns will have a wrinkly appearance once baked.
Divide the dough into 6 equal pieces. Working with one of the dough balls at a time, flatten the dough into a rough rectangle, fold the corners towards the center and pinch the seam shut. Flip the dough over, cup it with the palm of your hand and drag it on the surface in a circular motion until the seam on the bottom is completely sealed and the surface of the dough appears taut and smooth.
Arrange the dough on the baking sheet. Flatten the dough and cover with plastic wrap to prevent the dough from drying out.
Bring water to a boil and add in the baking soda into the hot water and stir until completely dissolved. Working with one portion at a time, dip the dough into the baking soda bath using a slotted spoon, so excess water can drip off.
Using the spoon or your fingertips, keep the dough submerged in the water for 1 minute. Transfer the dough to a wire rack and drain any excess moisture for a few minutes.
Return the dough to the prepared baking sheet.
Repeat with the remaining portions of dough. Arrange the dough a few inches apart to allow them to spread as they bake.
Using a lame fitted with a sharp blade or a paring knife, score an “X” on top of each bun. Sprinkle pretzel salt (or flaky salt) on top of the dough.
Bake the pretzel buns at 420°F for 5 minutes. Turn the temperature down to 375°F and continue baking for 10 to 15 minutes or until the buns appear a dark, golden brown and the center of the buns measure 190°F to 200°F when probed with an instant-read thermometer.
Brush the baked buns with butter (optional) and serve