In a saucepan, combine fresh or frozen blueberries, granulated sugar, vanilla extract, and lemon juice. Cook over medium heat while gently mashing the blueberries for 2-3 minutes until softened. Dissolve cornstarch in water and stir into the mixture, cooking for another minute until thickened.

Preheat your oven to 350°F (175°C). Combine graham cracker crumbs, sugar, and melted butter in a mixing bowl. Line a muffin tin with paper liners. Distribute 1½ tablespoons of the crumb mixture into each cup, press down to form a crust, and bake for 8 minutes until golden. Cool and reduce oven to 325°F (160°C).

Beat cream cheese and sugar with an electric mixer until smooth. Add vanilla, lemon juice, and lemon zest, mixing for another minute. Incorporate eggs one at a time, mixing only until just combined. Gently fold in sour cream.

Distribute 3 tablespoons of cheesecake batter into each muffin cup on top of the crusts. Add 1½ teaspoons of blueberry topping to each cheesecake, and swirl the sauce with a toothpick.

Bake at 325°F (160°C) for 18-20 minutes until the centers are slightly jiggly but set. Cool for 30 minutes, then refrigerate for at least 3 hours before serving.