Crush 2 Oreos into fine crumbs in a large microwave-safe mug (12-16 ounces). Break the remaining 2 Oreos into chunky pieces and set aside.
Add the flour, sugar, baking powder, and salt to the mug with the Oreo crumbs. Stir with a fork until evenly combined with no lumps.
Crack the egg into the mug and add the milk, oil, and vanilla extract. Whisk thoroughly with a fork for 30 seconds until the batter is smooth and no streaks remain.
Fold in half of the chunky Oreo pieces, reserving the rest for topping. The batter should be thick but pourable.
Press the remaining Oreo chunks gently into the top of the batter for a cookies and cream crown.
Microwave on high power for 60-90 seconds, checking at 60 seconds. The cake is done when the top looks just set with a few moist spots in the center.
Let the mug cake cool for 2 minutes before eating directly from the mug or carefully turning out onto a plate. The center will be wonderfully gooey and the edges perfectly set.
