Heat the oven to 350°F (175°C) and line baking sheets with parchment paper.

Beat the softened butter, granulated sugar, and brown sugar until creamy. Add the eggs one at a time, mixing after each addition, then blend in the vanilla.

In a separate bowl, whisk together the flour, baking soda, and fine salt. Gradually add the dry mixture to the butter mixture, mixing just until the dough comes together.

Fold in the semisweet chocolate chips. Scoop roughly 1/4 cup of dough for each cookie, flatten one portion, place an Oreo in the center, and cover it with another portion of dough.

Pinch the dough edges together completely and gently roll each stuffed cookie into a ball. Place the dough balls several inches apart on the prepared baking sheets, chilling them for 20–30 minutes if the dough feels soft.

Bake for 10–13 minutes, until the edges are lightly golden while the centers still look slightly underbaked. Cool the cookies on the baking sheet for about 10 minutes, then transfer them to a rack.