Add chilled heavy cream to a large bowl or the bowl of a stand mixer, along with the powdered sugar and vanilla extract.
Using an electric hand mixer or the whisk attachment for a stand mixer, whip the cream and other ingredients on medium-high speed until moderate peaks form, about 3-4 minutes. Stop the mixer and scrape down the sides of the bowl as needed.
You will know the whipped cream is ready when you can pull the whisk portion out of the whipped cream and it holds its shape for at least 30 seconds before falling.
Add about ½-1 cup of whipped cream to the center of a serving platter, spreading it down the middle into a 1 ½” wide rectangle.
Place a heaping spoonful of whipped cream on each chocolate wafer cookie, sandwiching them together in a log on top of the line of whipped cream on the serving tray.
Spread the remaining whipped cream on top of the line of chocolate wafer cookies, smoothing it out into an even layer so that it covers all of the cookies.
Wrap it gently with plastic wrap (try not to allow it to touch the cake) and place it in the fridge to chill for 8-12 hours.
Remove the zebra cake from the refrigerator and garnish it with shaved chocolate and fresh berries.
Slice the cake diagonally, creating striped pieces (like a Zebra), serve and enjoy.
Notes
Shortcut option: Use thawed frozen whipped topping (Cool Whip) in place of the homemade whipped cream.