Combine the graham cracker crumbs, brown sugar, and butter until thoroughly combined. Press evenly into the bottom and partially up the sides of the pan.
Bake for 10 minutes. Then set aside to cool while you make the filling.
To make the cheesecake filling:
Using an electric mixer on medium speed, beat the cream cheese, sugar, and sour cream until thoroughly combined and smooth. Mix in the eggs and vanilla.
Gently stir the blueberries into the batter.
Transfer the batter to the partially baked crust, and spread evenly.
Bake for 15 minutes at 350°F.
Reduce the oven temperature to 200°F (95°C). Bake for 2 hours or until the very center wobbles just a bit.
Remove the cheesecake from the oven, and gently run a thin knife around the outside edge.
Promptly return the cheesecake to the oven with the oven turned off, and leave for 2 hours.
Cover loosely and refrigerate overnight before serving.
Notes
Store in an airtight container in the refrigerator up to 3 days.