Preheat oven to 425F. Line baking sheet with parchment paper.
Divide pizza dough into few pieces. On a lightly floured surface, roll each into a rope about ½ inch thick, and then cut into 1 inch pieces.
Bring 2 quarts of water to a boil in a large saucepan. Add baking soda and pretzel pieces (depending on the size of your saucepan, you might need to cook in batches), and boil for 30 seconds, stirring constantly to prevent sticking.
Remove dough pieces with a slotted spoon and transfer to baking sheet. Brush with egg and sprinkle with coarse salt. Bake for 14−16 minutes, or until golden brown.
Meanwhile, in a small saucepan over low heat, melt butter and stir in flour. Cook for 2 minutes, stirring constantly.
Gradually whisk in milk and bring to a simmer. Stir in cheese and cook until the cheese has melted and the sauce is bubbly. Remove from heat and season with salt and pepper to taste.