Combine 2 cups (480ml) heavy whipping cream, 2 tablespoons powdered sugar, and 1 teaspoon pure vanilla extract in the bowl of a stand mixer or in a large bowl and beat with a stand mixer or electric hand mixer until the cream is thick and creamy with soft peaks; be careful not to overwhip.
Arrange a single layer of the 32 regular whole Oreo cookies in the bottom of an 8-inch square pan. Spread half of the whipped cream over the cookies and smooth with a spatula.
Add a second single layer of whole Oreo cookies, top with the remaining whipped cream, and smooth the top.
Sprinkle the 3 crushed Oreo cookies over the top, cover the pan tightly with plastic wrap, and refrigerate for at least 240 minutes or preferably overnight to set.
For clean slices, transfer the chilled cake to the freezer for 30 minutes before slicing.