I found this recipe years ago in one of my MANY cookie recipe cookbooks, and I've been making them ever since.
I use Andes Thin Mints and to make different variations, I just use the different Andes flavors.
Preheat the oven to 400 degrees F. Combine the butter, sugar, egg and vanilla extract in the bowl of an electric mixer. In a separate medium bowl, combine the flour, baking powder and salt using a whisk; set aside. Beat the butter mixture at medium speed until it is light and fluffy. Add the flour mixture, and beat at low speed until a soft dough forms.
Divide the dough in half. On a well floured surface, roll half of the dough into a 13x9 inch rectangle. Arrange the mints on the dough, evenly spaced, to form 7 rows of 7. Place the remaining half of dough between two sheets of wax paper and roll it into a 13x9 inch rectangle just like the first.
Remove the top sheet of wax paper, and invert the dough sheet over the mint topped dough; making sure to match up the edges. Use a pizza cutter, knife, or scalloped pastry wheel and evenly cut the dough between each mint. Press the edges of each pillow to seal.
Place the pillows 2 inches apart on ungreased or parchment covered cookie sheets. Bake for 10 minutes, or until the edges are a light golden brown. Place on a wire rack to cool completely. Store in an airtight container.