Prep the pan: Line the bottom of a 9-inch springform pan with parchment. Lightly spray the sides with cooking spray.
Preheat oven to 325°F (163°C).
Make the crust: Stir together crushed cookies, melted butter, sweetener, and a pinch of salt. Press firmly into the bottom of the pan using the bottom of a measuring cup. Bake for 8 minutes, then cool slightly.
Beat the cream cheese: In a large bowl, beat softened cream cheese on medium speed for 1–2 minutes until smooth.
Scrape the bowl often to avoid lumps.
Add yogurt and sweeteners: Mix in Greek yogurt, granulated sweetener, powdered sweetener if using, vanilla, salt, and cornstarch. Blend on low until just smooth. Do not overmix to avoid adding too much air.
Add eggs: Add eggs one at a time on low speed, mixing just until combined. Scrape the bowl and gently fold in the chopped cookies.
Fill the pan: Pour batter over the crust.
Tap the pan on the counter a few times to bring up any air bubbles.
Bake: Bake at 325°F for 40–50 minutes. The edges should be set, and the center should have a slight wobble. If it browns too quickly, tent loosely with foil.
Cool slowly: Turn off the oven, crack the door, and let the cheesecake cool inside for 30 minutes.
Then move to a wire rack and cool to room temperature.
Chill: Cover and chill in the fridge for at least 6 hours, preferably overnight. Slice with a warm, clean knife for neat edges.
Serve: Top with a small swirl of light whipped topping and a sprinkle of cookie crumbs. Enjoy cold.