Make the Blueberry Swirl:
In a small saucepan, combine blueberries, sugar, cornstarch, and water over medium heat. Stir frequently for about 5 minutes, until thickened. Slightly mash berries, then let cool.

Prepare the Cheesecake Filling:
In a bowl, beat together cream cheese, sugar, and vanilla extract until smooth. Set aside.

Make the Cookie Dough:
Cream butter, granulated sugar, and brown sugar until fluffy. Add egg and vanilla and mix well.
In another bowl, whisk flour, baking soda, and salt. Slowly add dry ingredients to the butter mixture until a soft dough forms.

Assemble the Cookies:
Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
Scoop 2 tbsp of dough per cookie onto the sheet, spacing them 2 inches apart.
Press a well into the center of each with your thumb.
Add a small spoonful of cheesecake filling into each well and swirl a bit of blueberry compote over it using a toothpick or knife.

Bake & Cool:
Bake for 12–15 minutes until edges are set and centers look slightly soft.
Cool for 5 minutes on the tray before transferring to a wire rack to cool completely.