In a medium bowl, beat the softened cream cheese using an electric mixer until smooth. Add the powdered sugar and vanilla extract, mixing until well combined. Place this mixture in the refrigerator to chill while you prepare the cookie dough.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Beat in the egg and vanilla extract until fully incorporated.

In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add this dry mixture to the butter mixture, mixing until just combined. Gently fold in the chocolate chips.

Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.

Using a cookie scoop or tablespoon, take a scoop of cookie dough and flatten it slightly in your hand. Place about 1 teaspoon of the cheesecake filling in the center and fold the dough around it. Roll it into a ball and place it on the prepared baking sheet, spacing them about 2 inches apart.

Bake for 10-12 minutes, or until the edges are golden but the center still looks soft. Remove from the oven and let them sit on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.