In the bowl of a stand mixer, dissolve the yeast, brown sugar, and salt in 1 1/2 cups of warm water. Allow the yeast mixture to activate for 10 minutes.
Attach your dough hook to the stand mixer. Add both the all-purpose flour and bread flour and mix on low speed for 5-6 minutes.
Remove the dough from the stand mixer and place it in a lightly oiled large bowl. Cover the bowl with plastic wrap and let the dough rise for approximately 1 hour or until the dough has doubled in size.
Once the dough has doubled in size, punch the dough down in the center, re-cover the bowl, and let the dough rise again for another 30 minutes.
Preheat the oven to 450 degrees. Line 2 baking sheets with parchment paper or Silpats.
Combine the remaining water and baking soda in a large skillet or saucepan. Bring to a boil over high heat.
Divide the dough into 12 pieces. Roll each piece into a 24-inch rope. Shape each rope into a pretzel shape.
Using a slotted spatula, gently dip each pretzel into the boiling water for approximately 30 seconds.
Remove the pretzels and place them on the prepared baking sheets.
Prepare an egg wash. In a small bowl, beat an egg with a fork. Using a pastry brush, brush the top of each pretzel with the egg wash. Sprinkle with kosher salt.
Bake for 8-10 minutes (or until the pretzels are golden brown) on the middle rack of the oven.
Transfer the pretzels to a cooling rack. Brush them with melted butter. Serve and enjoy!
Store homemade soft pretzels for up to 2 days in an airtight container.