In a microwave safe bowl, heat the butter in the microwave for 1 minute or until melted. Let it sit at room temperature for 5 minutes to cool down. Also, heat the water in the microwave for 40 seconds- 1 minute until 110°F. The water should be warm but not too hot.
Using a stand mixer with a dough hook, combine flour, brown sugar, yeast, and salt together. Add in the water and melted butter. Mix on low until dough starts to combine.
Then turn to medium and knead for 5 minutes. Halfway through, if the dough is very sticky add the extra ¾ cup of flour. Mix on low at first and then turn back to medium. The dough will be slightly sticky. It will become less sticky when it rises.
Place dough in a slightly greased large mixing bowl (spray with non-stick spray). Cover with a kitchen towel and let it rise for 1 hour until doubled in size.
Before rolling the dough, boil the hot water with the baking soda. Make sure there is plenty of room at the top of the pot because it bubbles a lot. Preheat oven to 450°F. Line 2 cookie sheets with silicone baking mats or parchment paper.
When the dough is ready, divide dough evenly in 12 balls using a kitchen scale. For each ball of dough, roll it out into 22-24 inch rope. It should be even thickness through the entire rope of dough. Make it into a thin U shape. Then twist it twice at the top and fold it over into pretzel shapes. Press the ends firmly into the pretzel. See photos above in post. Place pretzels on the cookie sheet. 6 per cookie sheet.
Place 2 pretzels at a time into the boiling water. Let it boil for 30 seconds. Take them out with a slotted spoon/spatula. Try to get as much water as you can off of the pretzel. Place the boiled pretzels back on cookie sheet. Continue until all pretzels are done.
Mix together the egg yolk and water to create an egg wash. Use a pastry brush to brush each pretzel with egg wash. Top with pretzel salt. As much as you desire.
Bake for 11-14 minutes. The pretzels are done when they are a deep golden color. Let it sit on the pan for 5 minutes before transferring to a cooling rack.