In a large bowl, cream together 1 cup softened unsalted butter and 1 cup granulated sugar using an electric mixer until light and fluffy, about 3-4 minutes. Add the egg and 2 teaspoons vanilla extract, mixing until fully combined.
In a separate bowl, whisk together 2 cups all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt. Gradually add the dry ingredients to the wet mixture, mixing on low speed until just incorporated. Avoid overmixing to keep the dough tender.
In another bowl, beat 1 cup softened cream cheese with 1/4 cup powdered sugar and 1 teaspoon lemon zest until smooth and creamy. Gently fold in the 1/2 cup fresh blueberries, being careful not to crush them.
Scoop out half of the cookie dough and spread it evenly in a parchment-lined baking sheet or a large mixing bowl. Dollop the cheesecake filling on top in spoonfuls. Then add the remaining cookie dough over the top. Using a knife or skewer, gently swirl the two mixtures together to create a marbled effect without fully blending them.
Using a cookie scoop or spoon, drop rounded tablespoons of the swirled dough onto a parchment-lined baking sheet, spacing them about 2 inches apart. Bake in a preheated oven at 350°F (175°C) for 12-15 minutes, or until the edges are lightly golden and the cheesecake swirl is set.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack. This resting time helps the cookies firm up and finish baking gently.