Dissolve the yeast in the lukewarm water. Whisk well until combined, about 1 minute.
To a mixing bowl add the butter, brown sugar, salt, and yeast mixture. Stir until combined. Slowly add in 3 cups of flour, 1 cup at a time. Mix by hand or use mixer fitted with dough hook, until dough is thick. Add 3/4 cup more flour and stir. If dough is still sticky, add flour, and additional 1/4 cup at a time, until no longer sticky, and dough bounces back when poked with your finger.
Turn dough out onto a lightly floured surface. Knead for 2 minutes and shape into a ball. Place in a large mixing bowl that has been lightly coated with nonstick spray. Cover and let rest for 10 minutes.
Meanwhile, bring a large pot of water to a boil with the baking soda, preheat oven to 425 degrees, and line two large baking sheets with parchment paper.
Section dough into six equal parts and roll each section into long ropes. Then, cut into 1-1/2 inch bites.
Once water is boiling, drop 10 pretzel bites into water and boil 20 seconds. Remove with a slotted spoon and place onto prepared baking sheets, making sure that pretzel bites do not touch. Repeat with remaining pretzel bites.
Brush beaten egg over each pretzel bite and sprinkle with salt. Bake for 12-15 minutes, until golden brown, rotating the sheet pans once halfway through cooking.
