Preheat your oven to 325°F (160°C). In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture into the bottom of a 9-inch springform pan to form an even layer.

Make the cheesecake filling

In a large mixing bowl, beat softened cream cheese with the remaining 3/4 cup sugar until smooth. Add sour cream and vanilla extract, mixing until well combined. Add eggs, one at a time, mixing on low speed until just incorporated.

Bake the cheesecake

Pour the cheesecake filling over the crust in the springform pan. Bake in the preheated oven for about 55-60 minutes or until the center is set but slightly jiggly. Turn off the oven and leave the cheesecake inside for 1 hour to cool gradually.

Prepare the berry compote

In a small saucepan, combine mixed berries, 1/4 cup sugar, and lemon juice. Cook over medium heat until the berries release their juices and the mixture thickens, about 10 minutes. Remove from heat and let cool.

Chill and serve

Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours or overnight. Before serving, top with the berry compote.