In a mixing bowl, combine the cold cream cheese, ½ cup granulated sugar, and 1 teaspoon vanilla extract. Using an electric mixer, beat until smooth and creamy. Set aside.
In a large mixing bowl, add 1 cup of barely softened unsalted butter, 1 cup of packed light brown sugar, and 1 cup of granulated sugar. Beat on medium speed until light and fluffy.
Incorporate the two large cold eggs and 1 tablespoon of vanilla extract into the butter-sugar mixture. Mix until well combined.
In another bowl, whisk together 3 cups of all-purpose flour, 1 teaspoon of baking soda, 1 teaspoon of cornstarch, and ½ teaspoon of fine sea salt. Gradually add this to the wet ingredients, mixing on low speed until just combined.
Gently fold in 1 cup of semi-sweet chocolate chips into the cookie dough using a spatula.
Cover the cookie dough with plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper.
Once the dough has chilled, remove it from the fridge. Take a portion of the dough, flatten it slightly, place about a teaspoon of cheesecake filling in the center, fold the dough around it, and roll into a ball.
Bake in the preheated oven for 12-15 minutes, or until the edges are golden brown.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.