In a mixing bowl, beat butter with an electric mixer until creamy, then blend in the egg, vanilla extract and peppermint extract.
Slowly add the dry mix and blend until all incorporated. Gather the dough into a ball and flatten into a disc. Wrap dough in plastic wrap and freeze for 20 minutes or until dough is firm.
Preheat oven to 350 degrees and remove dough from freezer. Line a baking sheet with parchment paper, set aside. Generously flour a flat surface and sprinkle the dough on both sides with flour. Roll out dough to 1/4 inch thick. Using a circle cookie cutter, 2 inches in diameter, cut out cookies and place on baking sheet at least one inch apart. If you do not have a circle cookie cutter, use the top of a small drinking glass
Bake for 12 minutes or until the edges of the cookies just barely begin to brown. Allow the cookies to cool on a baking sheet before transferring them to a cooling rack.
To make the frosting, combine the butter, yogurt and peppermint extract in a medium sized bowl. Slowly add the frosting mix and blend until smooth and creamy.
Once the cookies are cooled completely, frost half of each cookie and sprinkle with the crushed peppermint candies.