In a medium saucepan over medium-low heat, combine fresh blueberries, granulated sugar, lemon juice, vanilla extract, and cornstarch. Cook for about 15 minutes, mashing half the blueberries for a chunky texture. Let cool completely.

Preheat your oven to 350°F (175°C). Cream together unsalted butter, sugar, and vanilla extract until light and fluffy. Gradually add all-purpose flour and a pinch of salt. Press the dough into a greased 9x9-inch baking pan. Bake for 10 minutes until lightly golden.

In a large mixing bowl, beat room-temperature cream cheese and granulated sugar until smooth. Add cornstarch, sour cream, vanilla extract, and lemon zest. Incorporate the eggs one at a time.

Pour the cheesecake batter over the cooled crust. Spoon dollops of the cooled blueberry jam on top and swirl lightly.

Bake in the preheated oven for 38-42 minutes until center is slightly jiggly. Let cool in the oven with door ajar for 10 minutes.

Let the cheesecake bars cool completely in the pan on a wire rack. Refrigerate for at least 6 hours before cutting into squares.