Preheat the oven to 350°F and wrap the outside of a 9-inch springform pan with two layers of heavy-duty foil. Pulse 18 cookies, filling included, in a food processor into fine crumbs, add the melted butter and pulse again, then press firmly into the bottom of the pan.
Bake for 8 minutes, reduce the oven to 325°F and bring a kettle of water to a boil. Wipe out the food processor, add the cottage cheese and blend for 2 to 3 minutes, scraping down the sides, until completely silky.
Add the cream cheese, Greek yogurt, sugar, cornstarch, vanilla and salt and blend until smooth. Add the eggs and pulse just until combined.
Pour half of the filling over the crust and scatter half of the chopped cookies over it. Pour in the remaining filling and scatter the rest of the chopped cookies on top, pressing them in lightly.
Set the springform in a roasting pan, add hot water about 1 inch up the sides and bake for 60 to 70 minutes, until the edges are set and the center jiggles slightly.
Turn off the oven, crack the door and let the cheesecake cool inside for 1 hour. Remove from the water bath, loosen the edge with a thin spatula, cool to room temperature and refrigerate for at least 8 hours.
Whip the cold heavy cream with the powdered sugar to stiff peaks. Release the springform ring, pipe or spoon the whipped cream around the edge and finish with the crushed cookies.