Pre-heat oven to 325 degrees Fahrenheit. Butter the bottom of a spring-form pan.
In a double boiler, gently melt butter, Andes mints and chocolate. Stir until completely melted and smooth. Remove from heat and let cool.
Mix eggs, sugar and vanilla in a large bowl with an electric mixer at high speed until mixture becomes three times the original volume (about 3-5 minutes). Through a strainer, add 1/4 of the chocolate mixture into the bowl. Using a spatula, mix gently until thoroughly incorporated. Add remaining melted chocolate through strainer to catch any solid pieces and fold in gently until well mixed.
Pour batter into the prepared pan and bake for 12 minutes. The cake will be slightly soft to the touch, not firm. Don't be tempted to bake it for any longer than this. Remove from the oven and let cool in the pan. When cool, cover pan and refrigerate for 3 hours or overnight. Remove pan sides, invert cake onto large plate and remove pan bottom and peel away parchment paper. Invert cake again on another plate or serving platter. Sprinkle with confectioners' sugar or cocoa powder immediately before serving.
(Prep time includes overnight refrigerator time.).
*Can also use 56 Andes Toffee Crunch thins or 56 Cherry Jubilee Thins or 2 cups of Andes chips.