Prepare the Cake: Preheat oven to 350°F. Coat 3 (9-inch) round cake pans with baking spray, and line bottom of each with a piece of parchment paper cut to fit bottom.

Stir together hot coffee and chocolate chips in a medium bowl; let stand 2 minutes. Stir mixture until chocolate is melted, about 1 minute. Whisk in eggs, mayonnaise, and vanilla until smooth.

Stir together flour, sugar, cocoa, salt, baking soda, and baking powder in a large bowl. Stir in egg mixture. Pour batter evenly (about 1 3/4 cups per pan) into prepared pans.

Bake in preheated oven until a wooden pick inserted in center comes out clean, 18 to 20 minutes. Cool in pans 10 minutes. Remove cake layers from pans to wire racks, and let cool completely, about 1 hour.

Prepare the Frosting: Combine sugar and water in a medium saucepan over medium-high, and cook, stirring occasionally, until a candy thermometer registers 240°F, about 6 minutes.

Beat egg whites and cream of tartar in bowl of a stand mixer fitted with a whisk attachment on high speed until tripled in volume, about 3 minutes. With mixer running on low speed, gradually pour hot sugar mixture into egg white mixture. Add peppermint extract, increase speed to high, and beat until mixture is thick, white, glossy, and cooled to room temperature, about 12 minutes. Use immediately.

Spread frosting evenly between layers, and on top and sides of cake. Garnish top and sides with crushed peppermint candies, if desired. Loosely cover cake, and refrigerate up to 3 days.