Heat oven to 375°F. Line two baking sheets with parchment paper.
In the bowl of a stand mixer fitted with paddle attachment, mix cream cheese and confectioners’ sugar on medium speed until smooth, scraping down bowl as necessary. Transfer mixture to a small bowl and place in fridge while you make the cookie dough.
In a medium bowl, whisk together flour, baking soda, and kosher salt. Set aside.
Using the same mixing bowl and paddle attachment from step 2, beat butter and sugars on medium until light and fluffy. Add egg, egg yolk, and vanilla, mixing until thoroughly combined.
Add ⅓ of the flour mixture to wet mixture, mixing until it’s almost all incorporated. Scrape down bowl. Repeat two more times with rest of flour mixture.
Stir in chocolate chips.
Form dough into balls that are about 2 tablespoons each. (A medium cookie scoop is super helpful here.) Flatten each dough ball into a circle. Place half a tablespoon (1 ½ tsp) of cream cheese filling in the centre of each cookie. Form dough into a ball around filling, making sure the cookie is sealed. NOTE: Rather than trying to seal the cookies while they’re lying on the baking sheet, we found it easiest to pick up each cookie and form the dough into a ball around the filling in our hands.
Place on baking sheet, leaving 2" between each dough ball. Sprinkle cookies with sea salt, if desired.
Bake for 9–11 minutes or until cookies have set and edges are slightly golden.
Allow cookies to cool on baking sheets for a couple minutes, then transfer to wire rack to cool completely. (Although we certainly can’t blame you if you sneak one of these cookies while they’re still warm!)