Using an electric mixer on medium speed, beat the cream cheese and confectioners' sugar until thoroughly combined and smooth.
Cover and refrigerate.
To make the cookies:
Whisk together the flour, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the melted butter, brown sugar, and sugar until thoroughly combined. Mix in the egg, egg yolk, and vanilla. (You can instead mix by hand if you prefer.)
Reduce the mixer to low speed. Gradually add the flour mixture, mixing just until combined or a few streaks of flour remain. Stir in the chocolate chips.
Cover and refrigerate the dough for 2 hours or up to overnight.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Using a tablespoonful of dough at a time, flatten the dough into a thick disc. Place 1 & 1/2 teaspoons of filling in the center of the dough. Top with another tablespoon portion of dough that has been flattened.
Wrap the edges of the dough around the filling, pressing the edges to seal. Roll the dough into a ball between your palms.
Place the balls of dough on the prepared pans, leaving about 3 inches between each cookie. If your hands have warmed the dough, you may want to place the cookies back in the refrigerator for 10 to 15 minutes before baking.
Bake, one pan at a time, 15 to 18 minutes or until the edges are golden brown and the centers appear set. Refrigerate the remaining dough between batches.
Cool the cookies on the pan on a wire rack for 5 to 10 minutes. Then transfer the cookies off the pan to a wire rack to continue cooling.
Video
Notes
Store in an airtight container in the refrigerator up to 5 days. Bring to room temperature for serving.