Step 1: Make the Blueberry Compote

1. In a small saucepan, combine blueberries, sugar, and lemon juice.
2. Cook over medium heat for 3-4 minutes until the berries release their juices.
3. Stir in the cornstarch mixture and simmer for 1-2 minutes until thickened.
4. Remove from heat and let cool completely.

Step 2: Prepare the Cheesecake Swirl

1. In a small bowl, beat the cream cheese, sugar, and vanilla extract until smooth.
2. Set aside.

Step 3: Make the Cookie Dough

1. Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. In a medium bowl, whisk together flour, baking powder, and salt.
3. In a large bowl, cream the butter and sugar until light and fluffy.
4. Add the egg and vanilla extract, mixing until combined.
5. Gradually add dry ingredients to wet ingredients, mixing until a soft dough forms.

Step 4: Assemble the Cookies

1. Scoop tablespoon-sized portions of dough onto the baking sheet, spacing them 2 inches apart.
2. Make an indent in each cookie with a small spoon.
3. Spoon a small amount of cheesecake mixture into each indent.
4. Drizzle or dollop blueberry compote over the top.
5. Use a toothpick to swirl for a marbled effect.

Step 5: Bake

1. Bake for 10-12 minutes until edges are set and slightly golden.
2. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.