In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl using an electric hand mixer, beat the cream cheese until smooth. Add the powdered sugar, vanilla and salt, blending until smooth. Scrape down and transfer to a bowl, cover with plastic wrap and chill for a minimum of 1 hour.
In the same, bowl, cream together the butter, sugar and brown sugar until light and fluffy, approximately 3 minutes. Add in the eggs and vanilla until just combined.
Sift together the flour, baking soda and salt. Slowly add the dry ingredients to the wet ingredients until just combined. Fold in the chocolate chips. Cover and chill for a minimum of 1 hour.
When ready to assemble and bake, preheat the oven to 350°F and line a baking sheet with parchment paper.
Using a cookie dough scoop, scoop out a heaping tablespoon into well-floured hands. Press down with your palm to make them flat. Add a full teaspoon of the cream cheese mixture to center and then fold over the edges to seal it into the cookie dough. Place the ball onto the prepared baking sheet and using the bottom of a floured pint glass or other flat object, press down lightly until cookie is about 2 inches in diameter. Continue with remaining dough, keeping the cookie dough and filling chilled between batches.
Bake for 12 minutes or until the edges or lightly browned and set.
Remove and allow to cool on the cookie sheet for 2-3 minutes before carefully transferring to a wire rack using a spatula to cool completely.
If desired, sprinkle with flaky sea salt while still hot and tacky.
Notes
Note: keeping the dough well chilled is the key to making the filling stay inside the cookie dough!