Whisk all ingredients together until combined. Press into the bottom of a lightly greased 9-inch springform pan. Transfer to the freezer while preparing the filling.
For the filling
In a large bowl, whisk together pudding mix and milk. Transfer to the refrigerator to set according to package directions.
In the bowl of a stand mixer or a large bowl with a hand-held mixer, beat cream cheese and yogurt on medium speed until combined. Add vanilla and powdered sugar; mix well.
Once pudding has set, add to the cream cheese mixture and mix until incorporated. Pour over crust in springform pan and smooth with a spoon or offset spatula. Return to freezer.
For the whipped cream
Clean out stand mixer bowl and add the whisk attachment. (Or use another large bowl and a hand-held mixer.) Add heavy cream and whip on high speed. With mixer running, slowly add vanilla bean paste (or vanilla extract) and powdered sugar. Whip until soft peaks form.
Spread whipped cream over filling in springform pan. (If using any kind of non-fruit toppings, you could add them here!)
Freeze for 4-6 hours or overnight.
Let the cheesecake thaw at room temperature for 15-20 minutes and add fruit toppings and garnishes. (Alternately, if you'd like, you can add the whipped cream AND toppings just before serving.) Use a hot knife to cut into servings.