In a large mixing bowl or the bowl of a stand mixer, combine the chilled heavy cream, powdered sugar, and vanilla extract (if using). Beat the mixture on medium-high speed for approximately 5 to 7 minutes, or until stiff peaks form. The whipped cream should hold its shape but still appear smooth and light.

Using a 9x13-inch rectangular baking dish, arrange approximately 30 Oreo cookies in a single layer, covering the bottom entirely. Break a few cookies if needed to fill in gaps at the edges or corners.

Gently spread one-third of the whipped cream evenly over the layer of cookies, smoothing the surface with an offset spatula or the back of a spoon.

Add a second layer of Oreo cookies, followed by another layer of whipped cream. Repeat this once more, finishing with the remaining whipped cream on top as the final layer.

Cover the dish tightly with plastic wrap and refrigerate for at least 6 hours, or preferably overnight. This resting time allows the cookies to soften and meld with the cream for the proper icebox cake texture.

Immediately before serving, crush the remaining Oreo cookies and sprinkle them over the top layer for garnish. Slice and serve chilled.