In a microwave-safe mug (at least 12 ounces), whisk together the flour, sugar, cocoa powder, baking powder, and salt with a fork until no lumps remain.
Add the milk, oil, and vanilla extract to the dry ingredients. Stir gently with the fork just until the batter is smooth and no dry flour is visible, about 15-20 stirs. Do not overmix.
Drop the tablespoon of Nutella into the center of the batter. Use the back of a spoon to push it down slightly so it's submerged but not touching the bottom of the mug.
Microwave on high power for 60-90 seconds, depending on your microwave wattage. The cake is done when the edges are set and pulling away from the mug, but the center still looks slightly wet and jiggles when gently shaken.
Let the mug cake rest for 30 seconds to allow the center to stay molten and the edges to firm up. Serve directly from the mug with a spoon and enjoy while warm.