Combine the cream cheese, powdered sugar, and Oreo crumbs. Scoop 26 teaspoon balls of the cream cheese filling onto a parchment-lined baking tray. Chill the filling in the freezer until frozen solid.
Cream the butter, sugar, and brown sugar together for 3 minutes until light and fluffy.
Mix in the egg, egg yolk, and vanilla extract until just combined.
Mix in the flour, Oreo crumbs, salt, baking soda, and baking powder until just combined.
Scoop the dough with a 2-tablespoon cookie scoop. Press one of the frozen balls of cream cheese into the center and mold the dough around it to seal it in completely.
Roll the top and sides of each cookie dough ball in the extra Oreo crumbs, then place it on a lined baking sheet. Chill the cookie dough in the freezer for 3-4 hours minimum, overnight is best!
Preheat the oven to 350 F/180 C. Bake 10 cookies on a tray spaced 2-3 inches apart for 13-15 minutes. Let the tray cool on a wire cooling rack before removing them. If desired, make the cream cheese glaze. Combine the cream cheese and powdered sugar until smooth, then whisk in the vanilla and milk until thin. Drizzle over cookies!
Store leftovers in an airtight container at room temperature for 2-3 days. You can keep the cookie dough balls in the freezer for up to 3 months in an airtight container or freezer bag!