In a medium bowl, combine the room-temperature cream cheese and powdered sugar. Mix until perfectly smooth, making sure to scrape down the sides of the bowl. Cover the bowl and place it in the refrigerator to chill.
Cream Butter & Sugars: In a separate medium bowl, mix the butter, light brown sugar, and white sugar together until well combined.
Add Wet Ingredients: Add the egg, egg yolk, vanilla extract, baking soda, and salt. Mix for 1 minute until the mixture is fully incorporated.
Add the flour and mix just until combined. Gently fold in the semisweet chocolate chips.
Stuff the Cookies: Portion the cookie dough into large balls and flatten each one into a circle. Scoop about 1 teaspoon of the chilled cream cheese mixture into the center of the dough disk (the filling should be about half the size of the cookie). Carefully wrap the cookie dough around the cream cheese, sealing it completely, and roll it back into a ball.
Bake: Place the stuffed cookie dough balls onto a baking sheet, spacing them about 2 inches apart. Bake for 9–12 minutes, or until the edges are a beautiful golden brown. Let them cool slightly before enjoying!