Two nights (or more) before the day you plan to serve cheesecake, put the 1 1/4 cup Greek yogurt into a strainer lined with a cheesecloth. Position strainer on top of a bowl to catch the liquid that drains from underneath. Cover the yogurt with plastic wrap and set in the fridge overnight to allow liquid to drain. This will essentially create a cheese (labneh). After draining the yogurt, you should have around 270g left. You can discard the liquid.
The next day, line your 6 inch pan with parchment paper. Mix melted butter and graham cracker crumbs in a small mixing bowl. Transfer to your springform pan and press very firmly into the bottom to form a crust. Put in the fridge to chill while you prepare the filling.
In the bowl of a stand mixer fitted with a whisk attachment (or other mixing bowl, if using a handheld electric beater), place strained Greek yogurt, powdered sugar, lemon juice, and vanilla bean paste. Beat until well combined.
Add heavy cream and beat until entire mixture comes to stiff peaks. It should have the consistency similar to frosting.
Remove your cheesecake crust from the fridge and pour the filling into your tin on top of the crust. Use the back of a spoon or an offset spatula to smooth out the top. Cover with plastic wrap and return to the refrigerator to chill for at least 12 hours (overnight works great).
When ready to serve, swipe a toothpick along the sides of the cheesecake to separate it from the sides of the pan. Carefully remove the cheesecake from the springform pan and transfer to your serving platter (the parchment paper on the bottom of the crust should help with removing it from the bottom of the tin). Leftovers can be kept in an airtight container in the fridge for up to three days.