Arrange a rack in center of oven; preheat to 400°. In a large pot, bring 6 cups water to a boil.
Meanwhile, unroll crescent dough and separate into 8 triangles. Cut each triangle into 3 smaller strips. Wrap each sausage with a strip of dough, slightly overlapping and sealing the ends.
Carefully add baking soda to boiling water (it will bubble up). Using a slotted spoon, dip each wrapped sausage into boiling water for about 10 seconds, then transfer to a parchment-lined baking sheet.
In a small bowl, whisk egg with a splash of water. Brush sausages with egg wash. Sprinkle with coarse salt.
Bake pigs in a blanket until dough is golden brown, 15 to 18 minutes. Let cool slightly.
Arrange pigs in a blanket on a platter. Serve with mustard or cheese sauce alongside.