Prepare the baking sheets: Line 2 large baking sheets with parchment paper. Set aside.

Cream the butter and sugars: In a large bowl, beat the softened butter, granulated sugar, and brown sugar with an electric mixer on medium speed for about 2–3 minutes, until creamy and lighter in color.

Add the eggs and vanilla: Beat in the eggs one at a time, mixing well after each addition. Add the vanilla and mix until smooth. Scrape down the sides of the bowl as needed.

Combine the dry ingredients: In a separate bowl, whisk together the flour, cocoa powder, baking soda, and kosher salt until evenly combined and no large cocoa lumps remain.

Make the cookie dough: Add the dry ingredients to the butter mixture in two additions, mixing on low speed just until no dry streaks remain. Fold in the chocolate chips with a rubber spatula. Do not overmix; the finished dough should be thick and scoopable.

Chill the dough: Cover the bowl and refrigerate the dough for 30 minutes. Chilling makes the dough easier to handle and helps limit spreading.

Heat the oven: Toward the end of the chilling time, preheat the oven to 350°F (175°C).

Wrap the Oreos: Divide the dough into 24 roughly equal portions. Flatten one portion into a disk, place one Oreo in the center, and cover it with a second portion of dough. Pinch the edges together completely so the Oreo is fully enclosed. Roll gently between your palms to form a thick ball.

Arrange the cookies: Place 6 stuffed cookie dough balls on each prepared baking sheet, leaving about 2–3 inches (5–7.5 cm) between them. Gently press the tops just enough to slightly flatten them.

Bake until just set: Bake one sheet at a time for 11–13 minutes. The edges should look set while the centers still appear slightly soft and puffy. Avoid waiting for the centers to look completely firm, or the cookies may become dry.

Cool on the sheet: Let the cookies cool on the baking sheet for 10 minutes. They will continue setting during this time while remaining soft in the middle.

Finish cooling: Transfer the cookies to a wire rack and cool completely before storing. For the softest texture, serve them slightly warm or at room temperature.