Preheat your oven to 350°F (175°C). In a mixing bowl, combine cream cheese and powdered sugar to make the cheesecake filling.
In another bowl, cream together the butter, granulated sugar, and brown sugar. Add the egg, egg yolk, and vanilla extract, mixing until smooth. Gradually add baking soda, salt, and flour. Fold in the blueberries.
Drop spoonfuls of the cookie dough onto a baking sheet. Make a small indentation in the center of each cookie and fill with cheesecake mixture. Bake for 12-15 minutes.
Notes
You can substitute the blueberries with other fruits if desired. Store cookies in an airtight container.