2. Sift together the flour and cocoa powder and set aside.
3. In the bowl of an electric mixer, cream the butter, oil and sugar on high speed until light and fluffy. Stir in the vanilla.
4. Fold in half of the egg whites, then half of the flour-cocoa mixture, the remaining egg whites and finally, the remaining flour-cocoa mixture.
5. Spread the batter onto the prepared cookie sheet. Bake for 12 minutes or until set and springy to the touch.
6. Using a 3-inch round cookie cutter, quickly cut out 20 cookies before they have a chance to cool. Using a spatula, quickly transfer the hot cookies from the cookie sheet to a wire rack and allow to cool.
7. When the cookies are cool, spoon 1/3 cup of the frozen yogurt between 2 cookies. Repeat with the remaining cookies. Roll the edges of the ice cream sandwiches in the crushed peppermint candies so that the candies adhere to the ice cream.
8. Wrap each sandwich in plastic wrap and freeze until ready to serve. (These sandwiches may be made in advance and stored in the freezer for several weeks.)