Feed your potato flake sourdough starter approximately 8–24 hours before mixing the dough.
Add the flour, active starter, warm milk, sugar, and salt to the bowl of a stand mixer. Do not add the butter yet.
Using the dough hook, mix on medium speed until the dough begins pulling away from the sides of the bowl.
Cover and allow the dough to rest for 10 minutes.
Knead the softened butter into the dough by hand until it is completely incorporated.
Cover the dough and allow it to rise in a warm place until doubled in size, approximately 8–10 hours.
For easier handling, refrigerate the risen dough for approximately 2 hours. This step is optional but recommended.
Turn the dough onto a lightly floured work surface. Gently press out any large air bubbles and form it into a rough rectangle.
Roll the dough into a large rectangle approximately 5 millimeters thick.
Using a pizza cutter or sharp knife, cut the dough into strips and then into small rectangles.
Place one mini smoked sausage at the end of each rectangle and roll the dough around the center of the sausage, allowing the dough to overlap slightly.
Arrange seam-side down on a parchment-lined baking sheet.
Do not allow the shaped pigs in a blanket to rise a second time.
Preheat the oven to 375°F.
Bake on the middle rack for approximately 12–15 minutes, or until the dough is cooked through and lightly golden brown.
Serve warm with your favorite dipping sauces.