Preheat oven to 350 degrees.
Coat bottom of an 8-inch square baking pan with cooking spray.
Combine butter and mints in a 2-cup glass measure; microwave at high 30 seconds or until soft. Stir until smooth, and set aside.
Lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour, soda, and salt in a bowl. Combine sugar, cocoa, egg, and egg white in a large bowl; beat at medium speed of a mixer until well-blended. Add mint mixture; beat well. Add flour mixture; beat at low speed just until blended. Pour batter into prepared pan. Bake at 350 degrees for 20 minutes or until a wooden pick inserted in center comes out clean; cool completely on a wire rack.