Preheat your oven to 175°C (350°F). In a mixing bowl, blend the graham cracker crumbs, sugar, and melted butter until well combined. Press this mixture into the bottom of a springform pan. Bake for 8-10 minutes or until lightly golden.

Lower the oven temperature to 160°C (320°F). In a large bowl, mix the softened cream cheese until smooth, then mix in the sugar gradually. Add the eggs one at a time, beating well after each addition. Mix in the sour cream and lemon juice. Pour the filling into the cooled crust.

Prepare a water bath and bake the cheesecake for 60-75 minutes, or until the center is set but slightly jiggly. Turn off the oven and leave the cheesecake inside for 1 hour.

After an hour, remove the cheesecake from the water bath and let it cool to room temperature for 2-3 hours. Refrigerate for at least 6 hours or overnight to set fully.

While cooling, prepare the peach compote by cooking sliced peaches, sugar, and lemon juice in a saucepan until softened. Mix cornstarch with water and stir into the pan to thicken. Cool completely before using.

For the crumble, mix flour, oats, brown sugar, and salt in a bowl. Cut in cold butter until the mixture resembles coarse crumbs. Chill in the refrigerator for 15-20 minutes.

Spread cooled peach compote over the cheesecake and sprinkle crumble topping evenly. Preheat your oven to 190°C (375°F) and bake for 15-20 minutes or until crumble is golden brown.

Once baked, cool the cheesecake on a wire rack for 30 minutes. Refrigerate for a few hours. Let it sit at room temperature for 15-20 minutes before serving.