In a medium saucepan, combine fresh or frozen blueberries with sugar and lemon juice over medium heat. Gently mash the blueberries while cooking for about 5-7 minutes until soft and syrupy. Whisk together cornstarch and water, add it to the mixture, and let bubble for 1-2 minutes. Strain sauce to remove skins, then cool completely.

Preheat your oven to 325°F (163°C). Gather your muffin tin, ideally with 12 cavities.

In a medium bowl, combine graham cracker crumbs, sugar, and melted unsalted butter until well-blended. Press the mixture into the bottom of each muffin cavity to form an even crust. Bake for 5 minutes and cool completely.

In a large mixing bowl, beat the cream cheese and sugar together until smooth and creamy, about 2-3 minutes. Add in lemon juice, lemon zest, and vanilla extract, mixing until just combined. Incorporate the eggs one at a time.

Distribute the creamy filling evenly among the cooled crusts in the muffin tin. Drizzle a swirl of blueberry sauce over each cheesecake and gently swirl.

Place the muffin tin in the preheated oven and bake for 17-20 minutes. The edges should be slightly set with a jiggle in the center.

Remove the cheesecakes from the oven and let them cool at room temperature for about 15 minutes. Transfer them to the refrigerator to chill for at least 3-4 hours.