Mix softened cream cheese, powdered sugar, and 1 tsp vanilla extract in a bowl until smooth. Scoop small dollops onto a parchment-lined tray and freeze for 30 minutes.
Preheat oven to 350°F (175°C). Beat softened butter, brown sugar, and granulated sugar until fluffy (2-3 minutes).
Add eggs one at a time, mixing well after each. Stir in 2 tsp vanilla extract and mix until smooth.
Whisk flour, baking soda, and salt in a separate bowl. Gradually add to the wet ingredients, mixing gently. Fold in chocolate chips.
Scoop a portion of cookie dough, flatten slightly. Place a cheesecake dollop in the center and cover with more dough, sealing the edges.
Place cookies 2 inches apart on a baking sheet. Bake for 12-14 minutes until edges are golden and center is soft.
Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.