Preheat the oven to 350°F (175°C).

In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes. Let cool.

In a bowl, toss sliced peaches with sugar and lemon juice. Arrange the peaches over the cooled crust.

In a large bowl, beat the cream cheese and sugar until smooth. Add eggs one at a time, mixing well after each addition. Mix in vanilla extract. Pour the cheesecake mixture over the peach layer.

In a bowl, combine flour, brown sugar, and cinnamon. Cut in the cold cubed butter until the mixture resembles coarse crumbs. Sprinkle the crumble evenly over the cheesecake layer.

Bake in the preheated oven for 45-50 minutes, or until the center is set and the top is golden.

Allow the cheesecake to cool in the pan for about 30 minutes. Refrigerate for at least 4 hours or overnight before serving.