Preheat oven to 325°F (163°C). In a bowl, mix graham cracker crumbs, melted butter, and 3 tbsp sugar. Press into a greased 9-inch springform pan and bake for 10 minutes. Let cool.

In a saucepan over medium heat, combine blueberries, 1/4 cup sugar, and lemon juice. Simmer for 5 minutes until blueberries soften. Stir in cornstarch mixture and cook for another 2 minutes until thickened. Remove from heat and let cool.

In a large bowl, beat cream cheese and 1 cup sugar until smooth. Add eggs one at a time, mixing well. Stir in vanilla extract and sour cream until combined.

Pour the cheesecake filling over the crust. Drop spoonfuls of blueberry compote over the batter and swirl gently with a knife.

Bake at 325°F (163°C) for 50 minutes, or until the center is slightly set. Turn off the oven and let the cheesecake cool inside for 30 minutes with the door slightly open.

Refrigerate for at least 4 hours before slicing and serving.