Heat heavy cream, milk, cocoa powder, sugar, salt, and chocolate chips in a saucepan over medium-low heat until smooth and fully melted. Stir continuously to create a silky chocolate base without scorching the dairy.
Whisk egg yolks and cornstarch in a separate bowl until smooth. Slowly temper with warm chocolate mixture before returning everything to the saucepan. Cook gently while stirring until the custard thickens slightly.
Remove the saucepan from heat and stir in peppermint extract and vanilla extract. Allow the mixture to cool briefly so the mint flavor blends evenly without becoming overpowering.
Cover the custard with plastic wrap directly touching the surface and refrigerate until completely chilled and thickened for the best creamy consistency.
Fold mini chocolate chips into the chilled mixture, spoon into serving glasses, and chill again before topping with whipped cream, chocolate curls, crushed cookies, and mint leaves for serving.
