Mash the banana in a large microwave-safe mug (at least 12 ounces) with a fork until completely smooth with no lumps remaining.
Add the beaten egg, oil, vanilla extract, and sugar to the mug. Stir vigorously with a fork until fully combined and slightly frothy.
Add the flour, baking powder, cinnamon, and salt directly to the mug. Mix just until no dry streaks remain, being careful not to overmix.
Tap the mug gently on the counter 2-3 times to release any air bubbles and ensure the batter is evenly distributed.
Microwave on high power for 50-60 seconds, watching closely. The cake is done when the center is just set and springs back lightly when touched.
Let the mug cake rest for 30 seconds before eating. The texture will firm up slightly as it cools. Serve directly from the mug or invert onto a plate.