In a mixing bowl, beat the cream cheese, powdered sugar, and vanilla extract together until the mixture is smooth and creamy. Using a teaspoon or small scoop, portion the mixture into small balls and place them on a parchment-lined baking sheet. Freeze until firm.

In a large bowl, cream the softened butter, light brown sugar, and granulated sugar until the mixture becomes light and fluffy. Add the eggs and vanilla extract. Beat until fully incorporated.

In a separate bowl, whisk together the flour, cornstarch, baking soda, and salt. Gradually add the dry ingredients to the butter mixture. Mix just until combined. Fold in the semisweet chocolate chips.

Cover the cookie dough and refrigerate for a minimum of 2 to 3 hours, or overnight if preferred.

Scoop the chilled dough into tablespoon-sized portions. Flatten each piece slightly and create a small indentation. Place a frozen cheesecake filling ball in the center. Use another piece of dough to cover the filling completely, pinching the edges to seal. Shape into a smooth ball and arrange on a parchment-lined baking sheet, leaving space between each.

Preheat the oven to 350°F (175°C). While the oven preheats, refrigerate the prepared cookie balls to keep them firm.

Bake the cookies for 12 to 14 minutes, or until the edges are golden and the tops appear set. Remove from the oven and allow the cookies to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.

Serve once cooled and enjoy the delightful contrast of textures and flavors.