Preheat the Oven: Preheat your oven to 375°F (190°C). Lightly grease a 10-inch bundt pan or a large round baking dish with cooking spray or melted butter.
Prepare the Dough: On a surface dusted with flour, flatten the pizza dough to a thickness of approximately ¼ inch. Using a knife or a pizza cutter, cut the dough into small squares, roughly 2x2 inches, depending on the size of your smokies.
Wrap the Smokies: Place a lil’ smokie in the center of each dough square. Fold the dough around the smokie, pinching the edges to seal, and place it seam-side down in the prepared bundt pan. Repeat until all the dough squares and smokies are used. Arrange them evenly in the pan to create a layered, pull-apart effect.
Bake the Pigs in a Blanket: Brush the tops of the wrapped smokies with the melted butter. Bake in the preheated oven for 30-35 minutes, or until the dough is golden brown and cooked through.
Cool and Unmold: Allow the pull-apart pigs in a blanket to cool in the pan for about 10 minutes before inverting it onto a serving plate. Serve warm with the mustard cheese sauce.
Make the Roux: In a medium saucepan, heat the butter over medium heat until melted. Gradually add the flour, whisking continuously for about 1 to 2 minutes, until the mixture becomes smooth and starts to bubble, creating a roux.
Add the Milk: Slowly pour in the milk while whisking, and keep mixing until the mixture is smooth and starts to thicken, which should take about 3 to 4 minutes.
Add the Cheese and Mustard: Reduce the heat to low and stir in the shredded white cheddar cheese until melted and smooth.
Season and Serve: Season with salt and pepper to taste. If the sauce is too thick, add a splash of milk to reach your desired consistency. Serve the sauce warm alongside the pull-apart pigs in a blanket.