Line a 6-cup charlotte mold with heavy plastic wrap; set aside.
Cut angel food cake into 9 (1/4-inch) slices. Cut 4 slices diagonally in half; trim wide ends to fit into bottom of mold with points facing toward center. Cut remaining 5 slices in half crosswise and arrange around sides of mold. (Inside of mold should be completely covered.) Brush cake slices with 2 tablespoons liqueur; set aside.
Sprinkle gelatin over remaining 1/4 cup liqueur in a bowl; set aside. Combine 1/3 cup sugar, cornstarch, and cocoa in a saucepan. Gradually add milks, stirring with a wire whisk. Bring to a boil over medium-low heat. Cook 2 minutes or until thickened, stirring constantly. Beat egg yolks in a small bowl with a wire whisk. Gradually stir about one-fourth of hot mixture into yolks; add yolk mixture to remaining hot milk mixture, stirring constantly. Cook an additional 1 minute, stirring constantly. Remove from heat; stir in gelatin mixture, vanilla extract, and peppermint extract. Pour into a large bowl and place bowl over ice; let cool to room temperature, stirring frequently.
Beat egg whites and salt at medium speed of an electric mixer until foamy. Add 1/4 cup sugar, 1 tablespoon at a time, beating at high speed until stiff peaks form.
Gently fold one fourth egg white mixture into cocoa mixture. Gently fold remaining egg white mixture into cocoa mixture. Spoon mixture into prepared mold. Cover with plastic wrap; chill 8 hours.
To serve, remove plastic wrap. Place a serving platter on top of mold; invert charlotte onto platter. Remove mold; sprinkle top of charlotte with grated chocolate.