Preheat the oven to 350°F (180°C) and grease a 9-inch round cake pan.
In a large mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the crushed Oreo cookies.
Pour half of the batter into the prepared cake pan and spread it evenly.
Spoon Nutella onto the batter and swirl it using a toothpick or knife.
Cover the Nutella layer with the remaining batter, smoothing the top.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.