1. Cook the blueberries with sugar and lemon juice over medium heat until the berries burst and release their juices, lightly mashing as they soften.

2. Stir cornstarch with water, add it to the blueberry mixture, and cook briefly until thickened; strain for a smooth sauce and let it cool.

3. Heat the oven to 325°F and line a muffin pan with paper liners.

4. Combine graham cracker crumbs, sugar, and melted butter, then press the mixture firmly into liners to form the crusts.

5. Bake the crusts briefly until set, then let them cool while keeping the oven temperature the same.

6. Beat cream cheese and sugar until smooth, then mix in lemon juice, lemon zest, and vanilla until combined.

7. Add the eggs one at a time, mixing gently until incorporated.

8. Fill each crust with cheesecake batter and spoon a small amount of blueberry sauce on top.

9. Use a toothpick or knife to gently swirl the sauce into the batter.

10. Bake until the centers are just set and no longer wet.

11. Cool at room temperature, then refrigerate until fully chilled before serving.