Finely crush the Oreo cookies and mix them with the melted butter and milk until the mixture looks evenly moistened. Press it firmly into the bottom of a 20 cm cake pan. Place in the refrigerator while you prepare the filling.
In a mixing bowl, whip the cold heavy cream until it reaches a half-whipped stage.
Add the mascarpone, Philadelphia cream cheese, and Nutella. Continue mixing on high speed until the filling is smooth, thick, and fully combined.
Divide the filling into two equal parts.
In a shallow bowl, mix together the chocolate milk and coffee.
Dip each ladyfinger quickly into the chocolate milk and coffee mixture, then arrange the first layer over the chilled Oreo base.
Spread the first half of the filling evenly over the ladyfingers.
Add a second layer of dipped ladyfingers on top.
Spread over the remaining filling and smooth the top.
Refrigerate the cake for 2 to 3 hours.
For the topping, melt the Nutella with the coconut oil over a double boiler until smooth. You can also use 1 to 2 tablespoons of heavy cream instead of coconut oil if preferred.
Let the topping cool slightly, then pour it over the chilled cake and spread gently.
Return the cake to the refrigerator for at least 2 more hours, or overnight for the best texture.
Slice and serve chilled.