In a large bowl, cream together the softened unsalted butter, brown sugar, and white sugar until light and fluffy.

Add the room temperature eggs one at a time, mixing well after each. Stir in 2 tsp of vanilla extract.

In another bowl, whisk together the flour, baking soda, baking powder, and salt. Gradually add to the wet mixture until just combined.

In a medium bowl, beat the softened cream cheese with ¼ cup sugar until smooth. Mix in the egg yolk and ½ tsp vanilla extract until creamy.

In a saucepan, combine blueberries, 2 tbsp sugar, and lemon juice; cook until berries burst and syrupy. Stir in the cornstarch slurry and thicken.

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

Spoon cookie dough onto sheets, flatten, and make an indentation. Fill with cheesecake mixture and swirl blueberry topping.

Bake for 12-15 minutes or until edges are golden. Cool before transferring to a rack.