Cook sausages in a skillet over medium heat; remove from the pan and let cool.
Preheat oven to 400°F.
Cut puff pastry sheets into 24 rectangles slightly larger than sausages. Cut 12 thin slices of cheese slightly smaller than the pieces of pastry.
For each serving, place a slice of cheese in the center of a pastry rectangle and top with a sausage. Place another piece of pastry over the sausage. Fold down one corner and pinch the edges together.
Place on a baking sheet and bake for 12-15 minutes, or until pastry is golden and puffed.
Meanwhile, prepare the dipping sauce: Mix all ingredients together in a bowl.
Serve the pigs with the dipping sauce. Makes 12 servings.
Variation: Place each sausage link on the corner of a cheese-covered pastry square and roll up. This version requires half the amount of puff pastry.
*Brands may vary by region; substitute a similar product.