In the bowl of a stand mixer fitted with the knead attachment, combine the warm water, yeast, and brown sugar. Let the yeast bloom 5-10 minutes.
Add the salt, melted butter, and 2 cups of flour. Mix until all the flour is absorbed, then add ½ cup more flour at a time until a smooth and pliable dough.
Cover and let rise in a warm environment until doubled in size, about 1 hour.
Preheat the oven to 450F. Line two sheet pans with parchment paper.
Bring a large pot of water to a boil. Gradually add the baking soda as you stir to keep it from boiling over.
Divide the dough into 6-8 pieces. Roll each piece lengthwise into a log the size of the beef links.
Flatten the log enough to wrap around the beef link, pinch the edges together to seal.
Use a serrated knife to slice into bite-sized pieces. Repeat with remaining dough.
Reduce the stovetop heat to LOW. Working in small batches, boil the pretzel bites for 30 seconds, then use a slotted spoon to transfer to the prepared sheet pans.
While still moist, add salt to the dough portions of the pigs n blankets.
Bake for 10-15 minutes, until deeply golden brown, rotating the pan halfway through baking.