In a large bowl, beat the cream cheese with the powdered sugar and vanilla until smooth. In a separate bowl, whip the heavy cream to stiff peaks, then fold it into the cream cheese mixture.

Line a 9x5-inch loaf pan with plastic wrap. Quickly dip each Oreo in the milk, then arrange a single layer in the pan. Spread a thick layer of cream mixture on top. Repeat the layers, finishing with a cream layer. Cover and refrigerate at least 6 hours.

Unmold the cake onto a serving plate, peel off the plastic, slice, and serve cold.