Preheat the oven to 325°F (163°C) and line a muffin tin with paper liners.
In a small bowl, combine the graham cracker crumbs and melted butter. Mix until the crumbs are evenly coated.
Press about 1 tablespoon of the graham cracker mixture into the bottom of each muffin liner to form the crust. Bake for 5 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
Add the granulated sugar and vanilla extract to the cream cheese, mixing until well combined.
Add the egg and sour cream, mixing until just combined. Be careful not to overmix.
Pour the cream cheese mixture over the cooled crusts in the muffin tin, filling each liner about 3/4 full.
Bake for 18-20 minutes, or until the edges are set but the centers are slightly jiggly.
Turn off the oven and leave the cheesecakes inside for an additional 10 minutes. Then, remove from the oven and let cool to room temperature.
Refrigerate the mini cheesecakes for at least 2 hours before serving.
In a small bowl, combine the mixed berries, powdered sugar, and lemon juice. Gently toss to coat.
Top each mini cheesecake with the berry mixture just before serving.