Prepare Blueberry Swirl: In a small saucepan, combine blueberries, 2 tablespoons sugar, cornstarch, and water. Cook over medium heat, stirring occasionally, until mixture thickens (about 5 minutes). Mash berries slightly with a fork, then remove from heat and let cool completely.

Make Cheesecake Filling: In a small bowl, beat softened cream cheese with 1/4 cup sugar and 1/2 teaspoon vanilla extract until smooth and fluffy. Set aside.

Mix Cookie Dough: In a large bowl, cream butter with 1/2 cup granulated sugar and 1/4 cup brown sugar until light and fluffy (about 2 minutes). Add egg and 1 teaspoon vanilla, beating until well combined.

Add Dry Ingredients: In a separate bowl, whisk together flour, baking soda, and salt. Gradually fold dry ingredients into wet mixture, mixing just until no flour streaks remain. Don't overmix.

Shape Cookies: Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Scoop 2-tablespoon portions of dough and place them 2 inches apart on prepared sheets. Press your thumb into each dough ball to create a well.

Fill and Swirl: Spoon about 1/2 teaspoon of cheesecake mixture into each well, then add a small dollop of cooled blueberry mixture on top. Use a toothpick to gently swirl the two fillings together for a marbled effect.

Bake: Bake for 12-15 minutes, or until edges are set and lightly golden. Centers should look slightly soft. Let cookies cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.