Preheat your oven to 325°F (163°C) and line a 12-cup muffin tin with paper liners.
Combine graham cracker crumbs and melted butter in a medium bowl until well mixed.
Press a spoonful of the crust mixture into each muffin liner.
Bake for 8-10 minutes, or until slightly golden brown, then let cool completely.
Beat cream cheese and sugar in a large bowl until smooth and creamy.
Add eggs one at a time, mixing well after each addition.
Stir in vanilla extract, fresh lime juice, and lime zest.
Divide the cheesecake batter evenly among the muffin cups.
Spoon about 1 tablespoon of blackberry puree onto each cupcake, swirling gently.
Bake for 18-20 minutes, or until the edges are set and the center is slightly jiggly.
Cool completely in the tin before refrigerating for at least 2 hours.
Top with fresh blackberries just before serving.
