These are the ultimate snack—bite-sized, golden-brown nuggets of chewy, buttery pretzel perfection, served warm with a rich, creamy cheese dip that takes them totally over the top.
In the bowl of a stand mixer with a hook attachment, add the water, butter, brown sugar, yeast and salt. Mix until well combined. You can do this by hand if you need to- just use a sturdy wooden spoon to mix, and make sure it's mixed well. Let sit for 5 minutes.
Turn the mixer on low speed and add 1 cup of flour at a time. Add an additional ½ cup of flour to the mixture if the dough still seems sticky. Increase speed to medium and knead until the dough is smooth and pulls away from the sides of the bowl, 4 to 5 minutes. Sprinkle in more flour if the dough still seems sticky. Again-- you can do this all by hand if you need to. It'll take some arm strength to stir in the flour and knead the dough. Spray a large bowl with nonstick spray. Add the dough to the bowl. Cover loosely with a clean dishtowel and let rise in a warm place for about 1 hour.
Preheat the oven to 425℉. Line a large sheet pan with parchment paper.
Bring 3 quarts of water to a boil in a large saucepan. Sprinkle in the baking soda and return to a boil. While the water is preparing to boil, remove the dough from the bowl and flatten it into a disc. Cut it into 8 wedges. Roll each wedge into a 24-inch rope. Cut each rope into 1-inch pieces. Drop batches of the dough pieces into the boiling water for about 35 seconds. Then use a slotted spoon to transfer them to the prepared pan and spread them out so none of them are touching. Brush the egg wash over the tops of each boiled dough piece. Repeat with the remaining dough. Sprinkle with salt.
Bake until golden brown- 14 to 16 minutes. Cool before serving.
PREPARE THE CHEESE SAUCE:
In a small saucepan over medium heat, melt the butter. Whisk in the flour and cook for 30 seconds. Slowly whisk in the milk until no lumps of flour remain. Bring to a simmer (whisking constantly) over medium-low heat until it thickens, about 3 minutes.
Whisk in the shredded cheese until all of the cheese has melted. Serve immediately while warm- with the pretzel bites.