Preheat your oven to 325°F (160°C).

In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a springform pan to create an even layer (about 1 inch tall). Bake for 10 minutes, then set aside to cool.

In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add sugar and mix well. Then, add in the vanilla extract, eggs (one at a time), and lemon juice. Mix until fully combined and smooth.

Pour the cream cheese mixture over the crust in the springform pan. Bake for 50-60 minutes or until the center is slightly jiggly but set. Allow it to cool on a wire rack.

In a saucepan, combine fresh blueberries, sugar, cornstarch, water, and lemon juice. Cook over medium heat, stirring until the mixture comes to a boil and thickens. Remove from heat and let cool.

Once the cheesecake is cool, refrigerate it for at least 4 hours or overnight. Top with blueberry compote before serving.