Whisk the flour, salt and brown sugar in a large mixing bowl. Make sure there are no clumps of brown sugar. Whisk in the yeast. Melt the butter in a large bowl, then add the milk and warm water. Heat this mixture for a little bit in the microwave, or on the stove top. You just want it to be warm, not hot.
Pour milk mixture into the flour and stir with a spatula until just combined. Cover with a moist dish towel for 15 minutes and leave at room temperature for the first rise.
Lightly flour a surface and dump out the pretzel dough. Tuck the rough edges underneath and place in a lightly oiled large bowl. Rub about a tablespoon of vegetable oil onto the top of the dough to prevent cracking. Cover with a warm moist towel and let raise in a warm place for about an hour. For best results, we use our proofing setting on our oven, but you can also sit on top of your dryer!
Line 2 baking sheets with parchment paper.
Once the dough has doubled in size, transfer onto a lightly floured work surface. Divide the dough into 12 equal pieces. Dust your hands with flour, lay a piece of dough on the palm of one hand, tucking the edges under and roll it for about 10 seconds until its top is round and firm. You want to create surface tension so that your buns are not flat. Create dough balls by pinching the ends under and rolling in your hands. Place the balls onto a parchment -lined baking sheet with the smooth side up. Cover with plastic wrap and let raise for 20 – 30 minutes.
Preheat the oven to 425 degrees.
Make a baking soda bath by bringing 4 inches of water to a rolling boil in a large stockpot. Whisk in the baking soda.
Whisk together the egg yolk and 2 tablespoons of water.
Drop the buns, smooth side down, into the boiling water bath for 30 seconds. Using a slotted spoon, turn over for another 30 seconds. Use a strainer to remove the buns one at a time and place back onto the parchment.
Use a sharp knife to cut an “X” into the top of each roll. Brush with the egg wash and sprinkle coarse sea salt on top. Bake at 425 F. for 20 minutes. Rotate the pans halfway through. You will see a dark brown crust. Cool on wire racks for at least 30 minutes.