Like Thin Mints (the Girl Scout cookie) only better!
1/4 cup (1 stick) salted butter, softened
1/4 cup sugar
1 egg
1 tsp vanilla extract
1 1/2 cup flour
8 oz. white chocolate
1 tsp oil-based peppermint extract
~1 lb. bittersweet chocolate
Cream the butter and sugar. Beat in the egg and vanilla extract until smooth. Gently stir in the flour, just until thoroughly combined. Form the dough into a log about 1 inch in diameter, wrap in plastic wrap and chill until workable, ~1/2 hour.
Preheat oven to 325°F. Cut thin slices (about 1/8 inch thick) from the dough log, shape them into even disks, and lay them on ungreased cookie sheets. Bake until golden, about 7-10 minutes. Cool thoroughly.
Temper the white chocolate. Mix in the peppermint extract, stirring thoroughly to combine. You must use oil-based (also called "alcohol-free") extract, as the moisture in the other kind will cause the chocolate to seize. With a butter knife, carefully frost one side of each cookie with the minted white chocolate. If you have any leftover, use it to supplement any that didn't get a good, thick coat. Leave at room temperature until coating is thoroughly set.
Temper the bittersweet chocolate. Using clean dipping tongs (you'll need to stop and clean them frequently) dip the cookies in the bittersweet chocolate, turning and flipping to coat completely. Remove them and tap gently to remove excess chocolate, then let them set. The texture will be best the next day.