Beat the softened cream cheese, sugar, and vanilla with a hand mixer until smooth and creamy. Scrape down the sides to prevent lumps, then cover and refrigerate for at least 20 minutes so the filling firms up and is easier to handle.
Whisk the flour, baking soda, and salt together in a medium bowl. Set aside to ensure even distribution for soft, evenly baked cookies.
In a large bowl, beat the butter, brown sugar, and granulated sugar for 2 to 3 minutes until pale and fluffy. This step builds structure and tenderness in the dough.
Beat in the egg and vanilla until fully incorporated. The mixture should look smooth with a slight sheen.
Gradually add the dry ingredients to the wet mixture, mixing just until combined. Stop as soon as no dry streaks remain to avoid dense cookies.
Gently fold in the chocolate chips with a spatula, spreading them evenly through the dough.
Cover the dough and refrigerate for at least 30 minutes. Chilling helps control spreading and makes shaping easier. If the dough still feels sticky, chill longer.
Preheat the oven to 350°F and line baking sheets with parchment paper. Scoop about 1½ tablespoons of dough and flatten it in your palm. Place about 1 teaspoon of chilled cheesecake filling in the center, then fold the dough around it, sealing completely. Roll into a smooth ball and place on the baking sheet, leaving about 2 inches between cookies.
Bake for 10 to 12 minutes, until the edges are set and lightly golden while the centers remain soft. They will continue to set as they cool.
Let the cookies rest on the baking sheet for 5 minutes, then transfer to a wire rack. Serve cooled or slightly warm for a gooey cheesecake center.