Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large bowl, beat 8 ounces softened cream cheese and 0.5 cup softened butter until smooth and creamy.
Add 0.67 cup granulated sugar and 0.5 cup packed brown sugar; beat until light and fluffy. Add 1 large egg and 1 teaspoon vanilla extract and mix until combined.
Whisk together 1.75 cups all-purpose flour, 1 tablespoon cornstarch, 0.5 teaspoon baking soda, and 0.25 teaspoon salt in a separate bowl. Gradually add dry ingredients to the wet mixture and mix until just combined.
Fold in 1.5 cups semisweet chocolate chips until evenly distributed in the dough.
Prepare the cheesecake filling by beating 4 ounces chilled cream cheese with 0.25 cup powdered sugar and 0.5 teaspoon vanilla extract until smooth.
Scoop about 1.5 tablespoon portions of cookie dough and flatten slightly. Place a small spoonful (about 0.5 tablespoon) of cheesecake filling in the center and wrap dough around it, sealing well. Place cookies 2 inches apart on prepared baking sheets.
Bake for 10 to 12 minutes, or until edges are lightly golden and centers are set. Do not overbake to keep the cheesecake center creamy.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Notes
Store cooled cookies in an airtight container in the refrigerator for up to 5 days. Allow to come to room temperature before serving for the best texture.