Prepare the vanilla custard or pudding: In a large stainless steel saucepan, whisk well the egg yolks until homogeneous. Add the cornstarch and pour in just enough milk to dissolve the cornstarch and obtain a mixture mostly without lumps. Whisk in the rest of the milk, and the sweetened condensed milk. Cook over medium heat, stirring constantly until thickened (about 30 minutes). Here is how you can know the custard is ready: take the spoon you have been stirring it with and turn the back of the spoon to face you. Trace a path with your fingertip through the custard that is cleaving to the back of the spoon-- if the custard is ready, it will remain set along the sides of the path you traced. Stir in one teaspoon of vanilla extract. Spread about 1 cup of the custard at the bottom of a 3-qt. pyrex or baking dish and reserve.
Prepare the chocolate pudding: transfer half of the vanilla pudding or custard to a bowl. In a large cup, stir in cocoa powder with water until dissolved. Add to the half of the vanilla pudding in the saucepan and whisk well over low heat until the mixture is homogeneous and smooth (about 2-5 minutes). Reserve!
Place 2 cups of milk into a medium bowl. Stir in about 2 tablespoons of sugar (or more if desired) and 1 teaspoon of vanilla extract and then moisten the Oreo cookies one by one. SEE PIC. 1 As you moisten them on both sides and shake quickly to remove excess liquid, layer them on top of the spread vanilla custard. SEE PIC. 2 Make sure to form one single layer, not leaving much space in between the cookies.
Pour and spread all the remaining vanilla custard on top of the layer of cookies. Then moisten more cookies, shake off excess liquid, and distribute on top to form a single layer. Pour all the chocolate custard on top and spread well. SEE PIC. 3 Let Oreo trifle set and mostly cool at room temperature. Then prepare the white cream.
To prepare the white cream, beat softened cream cheese with powdered sugar at medium speed until homogeneous and smooth (about 1 minute) using an electric mixer. Add the heavy cream and 1 teaspoon of vanilla extract and beat until smooth and creamy (about 1 minute). SEE PIC. 4 Pipe onto cool trifle. If desired, sift just a little bit of cocoa powder on top. Alternatively, you may skip the cream cheese and simply beat 2 cups of heavy cream, powdered sugar, and vanilla extract at medium speed until obtaining a sweet whipped cream. Then spoon over the cool trifle and gently spread to form a single layer.
Cover Oreo trifle with foil or plastic wrap and refrigerate until chilled, at least 4 hours or overnight. Serve and enjoy!