Line a small baking sheet or plate with parchment paper. In a small bowl, use a whisk or mixer (depending how hard your cream cheese is) to mix the cream cheese with powdered sugar until smooth and combined.
Place 10-12 heaping teaspoons of cream cheese on the baking sheet or plate. Freeze for at least one hour, or until frozen almost completely solid.
Measure out your Oreo crumbs, or make your own by finely chopping 6 Oreo cookies, or placing them in the food processor or blender until crumbs form. You can also add the Oreos to a ziploc bag and roll over them with a roll pin until you have fine crumbs. Roughly chop the remaining 6 Oreo cookies.
When the cream cheese is frozen almost solid, line two large baking sheets with parchment paper and set aside. Whisk together flour, salt, and baking soda then set aside. In the bowl of a handheld mixer or standing mixer, beat the butter and sugars together until light and fluffy (about 1-2 minutes). Mix in the egg, egg yolk, and vanilla extract. Add in flour, salt and baking soda and mix until combined. Add in the white chocolate chips, Oreo crumbs, and crushed Oreos.
Scoop 12 heaping tablespoons of dough onto each baking sheet. They should be fairly big - if measured they'd be about 2 tbsp-sized (these are big cookies!). Press the back of a teaspoon slightly into the top of half the balls of dough to create an indent.
Remove the cream cheese filling from the freezer and place one into each of the cookies. Take a second ball of dough and place it over the cream cheese, pinching the sides to seal the cream cheese inside (see picture in post above), but making sure to not squish the cream cheese into the cookie dough.
Refrigerate the prepared cookie dough balls and repeat with the second cookie sheet and remaining dough. Preheat the oven to 350°F and leave the cookie dough in the fridge while it preheats.
Bake the cookies in the preheated oven one sheet at a time for 13-17 minutes, or until the edges are slightly golden brown and the tops are set. Remove from the oven and leave them on the baking sheet for 10-15 minutes, then transfer to a cooling rack to cool completely.