Preheat oven to 350°F and lightly grease a large oven-safe mug or ramekin.
In a medium bowl, whisk together the flour, granulated sugar, brown sugar, cocoa powder, baking powder, and salt.
Add the vegetable oil, milk, Greek yogurt (or sour cream), and vanilla extract. Stir until just combined.
Fold in the crushed Oreo cookies and mini chocolate chips.
Pour the batter into the prepared mug or ramekin and gently smooth the top.
Sprinkle a few extra crushed Oreo pieces and mini chocolate chips over the batter.
Bake for 18–22 minutes, or until the center is set and a toothpick inserted into the cake comes out with a few moist crumbs.
Let the mug cake cool for 5–10 minutes.
Top with whipped cream and additional crushed Oreo cookies before serving.