In a food processor, blend the graham crackers together until finely ground Pour into a bowl, then add in the sugar and mix to combine.
To the bowl, pour in the butter and mix until it forms a sand-like texture.
Press into a prepared 8x8 pan using the back of a measuring cup (preferably a ⅓ cup) until set. Chill in the freezer for 30-45 minutes.
For the Filling
In a separate bowl, whisk together the cream cheese, greek yogurt, and vanilla extract using a hand mixer or stand mixer.
Last, gently pour in the powdered sugar, then whisk again until the powdered sugar is fully incorporated and the cheesecake filling is smooth and fluffy.
Add the cheesecake filling to the set graham cracker crust, smoothing the filling out with an offset spatula or the back of a large spoon.
Place in the fridge for up to 5-6 hours, or overnight.
Notes
Keep it Room Temperature - For the smoothest texture and taste, make sure the cream cheese and greek yogurt are completely room temperature before whisking them together.Add the Powdered Sugar, Gently! - Powdered sugar is known for flying everywhere, so be gently when pouring it into the bowl with the cream cheese and yogurt. Whisk on a low speed, then increase the speed as the powdered sugar becomes incorporated.