Start with very cold heavy cream and a cold mixing bowl. I put my bowl in the freezer while I gather the other ingredients. Metal bowls work best.
Add the heavy whipping cream to your cold mixing bowl and whip until stiff peaks form. I use a stand mixer, but a hand mixer works fine too. Let this sit in the refrigerator while you move on.
Add the mascarpone cheese, powdered sugar, vanilla, Kahlúa, cold espresso, and cocoa powder to another large bowl and mix until smooth and thick, which should take 2 to 3 minutes.
Add the cold, whipped cream to the mascarpone mixture and fold until thoroughly combined. Use a spatula to do this, so the dip stays nice and fluffy. Using a whisk will deflate the whipped cream and ruin the consistency, which should be more like a mousse.
Return the dip to the refrigerator and let it chill for at least an hour before serving. You want this to stay cold, which will help it stay nice and thick.
Just before serving, spoon it into your serving bowls and sprinkle the shaved chocolate on top. (you can also spoon it into your serving bowls before you chill it)