In a small saucepan, combine blueberries, sugar, cornstarch, and water. Cook over medium heat, stirring occasionally, until thickened (about 5 minutes). Mash slightly and let cool completely.

In a bowl, beat cream cheese, sugar, and vanilla until smooth. Set aside.

Cream the butter, granulated sugar, and brown sugar until light and fluffy. Add egg and vanilla; mix well.

In a separate bowl, whisk flour, baking soda, and salt. Add dry ingredients to wet, mixing until a soft dough forms.

Preheat oven to 350°F (175°C). Line baking sheet with parchment paper.

Scoop dough into 2-tablespoon portions and place on the tray, 2 inches apart. Use your thumb or the back of a spoon to make a small indentation in each cookie.

Spoon a small amount of cheesecake filling into each indentation. Top with a small spoonful of blueberry swirl and gently swirl the two with a toothpick or knife.

Bake for 12–15 minutes, or until the edges are set and the centers are slightly soft. Cool on the tray for 5 minutes before transferring to a wire rack.