Add the heavy whipping cream, powdered sugar, and vanilla extract to a large bowl. Use the whisk attachment on an electric mixer and whisk until the whipping cream has formed stiff peaks. Set aside.
Dip each chocolate sandwich cookie in the milk before placing half of them in an even layer across the bottom of a 9x9 inch pan. (If you're skipping the dipping step, just place the cookies in the pan, forming an even layer to cover the bottom.)
Spread half of the whipped cream evenly over the layer of chocolate sandwich cookies. Carefully add the chocolate pudding layer and spread it evenly over the whipped cream.
Dip the remaining cookies in the milk and then layer them over the chocolate pudding. Top with the remaining whipped cream and spread it evenly over the chocolate sandwich cookies. Cover with plastic wrap and refrigerate at least 6 hours, preferably overnight.
Before serving, drizzle with chocolate fudge sauce and crushed chocolate sandwich cookie pieces (optional). This should be kept refrigerated until ready to serve and leftovers should be stored in the refrigerator up to 5 days.
Notes
Regular Oreos can be used in place of the gluten free chocolate sandwich cookies if you don't need it to be gluten free.
Dipping the chocolate sandwich cookies in milk before placing them in the pan will give them a softer, more cake-like texture. If you choose not to dip them in the cake, the cookies will still have a bit of a "bite".