In a large mixing bowl, whisk the yeast into the warm water. Let the mixture sit for 5 minutes. Add salt, brown sugar, and melted butter to the bowl and whisk until combined.
Slowly add flour, one cup at a time. Using the dough hook attachment on a stand mixer or a wooden spoon if manually mixing in the flour, mix until dough is thick and no longer sticky. Mix until there is no crumbles left in the bottom of the bowl. If using a stand mixer the dough will pull away from the sides of the bowl. If it is still sticky, add more flour one tablespoon at a time, mixing thoroughly between each addition of flour, until the dough is not sticky. You should be able to poke the dough with your finger - if it bounces back, it is ready to knead.
If using stand mixer, continuing kneading the dough with the dough hook for 5 minutes on medium-low. If you are not using a stand mixer, turn the dough out onto a lightly floured surface. Knead the dough for about 5 minutes, then shape into a ball. Place in a large greased mixing bowl. Cover and let the dough rest in a warm area for an hour. The dough should double in size.
Preheat oven to 425°F. Line two large baking sheets with parchment paper or silicone baking mats. Set aside.
Transfer the dough ball onto a cutting board and cut the dough into 6 sections. Roll the dough into six 20-inch long ropes. Cut the rope into 1.5 inch pieces to make bites.
In a large pot, bring 8 cups of water and the baking soda to a rapid boil. Boil 15-20 pretzel bites at a time, for 30 seconds. They will increase in size. Remove with a large slotted spoon and place onto the prepared baking sheet. Make sure the bites aren't touching.
Brush beaten egg over the top of each pretzel bite. Sprinkle with sea salt. Bake batches for 15 minutes each, or until golden brown. Only bake one pan at a time.
Remove from oven, transfer to a wire rack and let cool 5 minutes before eating.
Notes
Note: This recipe will make about 90 Homemade Pretzel Bites. They will remain fresh for up to 3 days in an airtight container.