Step 1: Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper.
Step 2: In a medium bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
Step 3: In a large bowl, cream together the softened butter, ¾ cup granulated sugar, and brown sugar with an electric mixer until light and fluffy (about 2-3 minutes).
Step 4: Beat in the eggs one at a time, mixing well after each addition. Stir in 1 teaspoon vanilla extract.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Step 6: Gently fold in the blueberries. If using frozen blueberries, ensure they are lightly tossed in 1 tablespoon of flour first.
Step 7: In a separate small bowl, prepare the cheesecake swirl by beating together the softened cream cheese, ¼ cup granulated sugar, egg yolk, and ½ teaspoon vanilla extract until smooth and creamy.
Step 8: Drop spoonfuls of cookie dough onto the prepared baking sheets, about 2 inches apart.
Step 9: Using a small spoon or a piping bag, dollop about ½ teaspoon of the cheesecake mixture onto the center of each cookie dough ball. Use a toothpick or the back of the spoon to gently swirl the cheesecake into the cookie dough.
Step 10: Bake for 12-15 minutes, or until the edges are lightly golden and the centers are just set. The cheesecake swirl might still look slightly soft but will firm up as it cools.
Step 11: Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.