Beat cream cheese until smooth. Add dulce de leche and vanilla and mix only until evenly combined.
Layer:
Combine cooled coffee and milk in a shallow dish. Dip biscuits one at a time for 1 to 2 seconds.
Arrange a single biscuit layer in the dish, spread with one-quarter of the cream, and repeat to make four biscuit layers and four cream layers. Smooth the top.
Chill and Serve:
Cover and refrigerate for at least 6 hours, preferably overnight. Dust lightly with cocoa and cut with a warm clean knife.
Notes
Use firm rectangular chocolate tea biscuits rather than soft cookies.