Prepare the Blueberry Swirl:

1. Cook the Blueberries:
   • In a small saucepan, combine blueberries, sugar, cornstarch, and water. Cook over medium heat, stirring occasionally, until the mixture thickens (about 5 minutes).
   • Remove from heat, mash the blueberries slightly, and let cool.

Make the Cheesecake Filling:

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

Prepare the Cookie Dough:

3. Mix the Dough:
   • In a large bowl, cream the butter, granulated sugar, and brown sugar until light and fluffy. Add the egg and vanilla extract, mixing until combined.
   • In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough forms.

Assemble the Cookies:

4. Form the Cookies:
   • Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop 2-tablespoon-sized portions of dough onto the baking sheet, spacing them 2 inches apart.
   • Use your thumb or the back of a spoon to make a small well in the center of each dough ball.
5. Add the Fillings:
   • Spoon a small amount of the cheesecake filling into each well, followed by a small dollop of the cooled blueberry swirl. Use a toothpick or knife to gently swirl the two together for a marbled effect.
6. Bake:
   • Bake the cookies for 12-15 minutes, or until the edges are set and the centers are slightly soft. Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.