Place the Oreos in a food processor and pulse until finely ground. Transfer to a bowl and add the melted butter. Stir until all crumbs are coated and the mixture holds its shape when pressed together.
Press crust into the bottom of a 9-inch springform pan and slightly up the sides. Chill in the refrigerator while preparing the filling.
To make the filling:
Place the chocolate chips in a microwave-safe bowl and heat in 30 second intervals, stirring after each, until melted and smooth. Set aside to cool. (You can even do this step before you prepare the crust to give it more time to cool before using.)
In a large bowl with an electric mixer (or the bowl of a stand mixer), beat cream cheese and Greek yogurt on medium speed until smooth. Add powdered sugar and vanilla; mix until incorporated. Add melted chocolate and mix well.
In another bowl, either with a hand-held mixer with the whisk attachment, or the bowl of a stand mixer with the whisk attachment, whip heavy cream until stiff peaks form. Fold whipped cream into the cream cheese mixture until no streaks remain (your arm might get tired!). Fold in the chopped Oreos.
Pour filling into the prepared springform pan over the crust and spread to the edges. Cover with plastic wrap and freeze 4 to 6 hours, or overnight. Thaw for 30 minutes in the refrigerator before serving. Garnish with additional whipped cream and Oreos, if you’d like!