Preheat your oven to 180C. Cover the bottom and sides of your 8" springform pan with aluminum foil.
Combine the melted butter and crushed cookies in a small bowl. This mixture should have the consistency of wet sand.
Press it down evenly at the bottom of the pan. Bake for 10 minutes. Lower the oven temperature to 160C while you're preparing for the filling.
Cheesecake Filling
Soften the cream cheese using a spatula, in a large bowl.
Add the sugar. Mix well.
Now whisk in 2 eggs, Greek yogurt, vanilla extract, and 1/3 cup all-purpose flour.
Mix well until smooth and creamy.
Toss the diced peaches with 2 tsp of flour and fold into the batter.
Pour into the prepared crust. Place some extra chopped peaches on top if you wish.
Carefully place in the oven and bake at 160C for 55-60 minutes. The top of the cake should look cooked and the center should be a bit wobbly. My cake took 60 minutes.
Turn off the heat and slightly crack the door open and allow it to cool for 60 minutes.
Let the cake cool on the countertop for another hour and then refrigerate for at least 8 hours for it to set completely. Remove carefully from the pan, and place it on your serving plate.
Spoon over the peach compote and top with a couple of basil leaves.
Slice and enjoy!
Peach Compote
Combine diced peaches, water, sugar, and half a vanilla bean in a small saucepan.
Cook on medium heat until the peaches are soft and cooked through.
Take the pan off the heat and add a tablespoon of rum. This is completely optional. Let cool before topping the cheesecake.