Prepare a baking dish by lining it with parchment paper.
Combine cream cheese and dulce de leche in a bowl until smooth.
Dip each chocolate cookie briefly in milk.
Layer the bottom of the dish with the soaked cookies.
Spread a layer of the cream cheese mixture over the cookies.
Repeat layers, alternating between cookies and cream mixture.
Finish with a layer of the cream mixture on top.
Cover the dish with plastic wrap and refrigerate for at least 4 hours.
Once set, carefully remove from the dish and slice.
Garnish with chocolate shavings before serving.