Adjust the oven rack to the middle position, and heat the oven to 400°F. Line a rimmed baking sheet with parchment paper. Unfold the puff pastry on a lightly floured counter and roll into a 12x9-inch rectangle with the short side parallel to the edge of the counter, flouring the top of the dough as needed.
Using a sharp knife or pizza wheel, trim the dough down to a 12x8-inch rectangle. Cut the dough lengthwise into eight 1-inch strips. Cut the dough crosswise at three 3-inch intervals. You should have thirty two 3x1-inch dough strips.
Lightly brush 1 row of dough strips with egg wash. Roll 1 frank in each dough strip and transfer the bundle, seam-side-down, to the prepared sheet. Repeat with the remaining dough strips and franks, spacing the bundles ½-inch apart.
Combine the Parmesan, bagel seasoning and pepper in a bowl. Working with a few bundles at a time, brush the tops with egg wash and sprinkle with the Parmesan mixture. Bake until the pastry is golden brown, about 23 minutes.
MAKE THE SAUCE:
In a bowl, whisk together all of the sauce ingredients.
Let the pigs cool on the baking sheet for 10 minutes. Serve with the mustard sauce.