Crush 2 Oreos into small pieces using your hands or a knife. Set aside the third cookie for topping.
In a 12-16 ounce microwave-safe mug, combine the flour, sugar, cocoa powder, baking powder, and salt. Stir with a fork until no lumps remain.
Add the milk, oil, and vanilla extract to the dry ingredients. Mix thoroughly with the fork, scraping the bottom and sides of the mug to incorporate all the dry mixture. The batter should be smooth and pourable.
Fold in the crushed Oreos, reserving a few pieces for the top if desired. The batter will look thin but will thicken slightly as it sits.
Crush the remaining Oreo and sprinkle the pieces on top of the batter for decoration and extra texture.
Microwave on high power for 60-90 seconds. Start checking at 60 seconds — the top should look just set with a few moist spots. If the center is still liquidy, continue in 10-second bursts until done.
Let the mug cake rest for 1-2 minutes to finish cooking through and cool slightly before eating. The center will be fudgy and warm. Top with ice cream or whipped cream if desired and enjoy immediately with a spoon.