In a large bowl, combine the first 4 ingredients. Cut in butter and shortening until mixture resembles coarse crumbs. Beat egg and milk. Stir into dry ingredients until a soft dough forms; dough will be sticky.
Turn onto a generously floured surface; knead 6-8 times or until smooth, adding additional flour as needed. Roll out to 1/4-in. thickness. Cut with a 2-1/4-in. biscuit cutter. Fold each dough circle over a hot dog and press edge to seal. Place on greased baking sheets.
Bake at 450° until golden brown, 10-12 minutes. In a small bowl, combine the sauce ingredients. Serve with corn dogs.