Note: Make the dough 1 day ahead of when you plan to slice and bake the cookies.
On waxed paper, sift together flour, baking powder and salt. In double boiler, over hot, not boiling, water, melt chocolate, remove from heat. (Or melt chocolate in microwave-safe bowl at High 3 to 4 minutes, stirring twice.)
In large bowl, with electric mixer at medium speed, beat butter, sugar, egg and vanilla until light and fluffy. Beat in melted chocolate until smooth. With wooden spoon, stir in dry ingredients and nuts; mix well. Wrap in plastic wrap; chill ½ hour while making mint dough.
On waxed paper, sift together flour, baking powder and salt, in large bowl, with electric mixer, beat butter, sugar, egg, mint extract and food color until smooth and fluffy. With wooden spoon, stir in the dry ingredients, add cherries, mix well.
Divide chocolate dough in half. Shape each into a ball, flatten. Place each half between two sheets of waxed paper. On lightly dampened surface, roll each half into an 8-inch square. Roll mint dough between paper into an 8-inch square, making corners perfect.
Place one chocolate square on cookie sheet; peel off paper on top. Peel top paper off mint square; flip mint square onto chocolate square; peel off paper; press lightly. Layer other chocolate square over mint square. Be sure all sides are even. Cover with foil; refrigerate.
Day of Serving:
Preheat oven to 350 degrees F. Remove foil; cut square into 3 strips. (Refrigerate 2 strips until ready to cut.) Cut each strip crosswise into ¼ inch slices.
Bake on greased cookie sheets 10 minutes, or until set. Cool on rack; store in container.