Mix all dry ingredients together in a 12 oz microwave safe mug.: As you stir the all purpose flour , brown sugar , white sugar , baking powder , cinnamon , nutmeg , and a pinch salt , notice how the dry mixture looks uniform, with the spices speckling the lighter flour. This homogeneity ensures even flavor and lift, and failing to blend well can lead to pockets of baking powder or sugar which produce uneven texture and tiny bitter bites. A good sign is a visually even mixture with no concentrated clumps, and the aroma of warm spice will start to come through even before you add liquids. Avoid overworking this stage, gentle but thorough mixing is best.
Stir in the shredded carrots, vanilla and milk. Mix well, especially the bottom so there is no dry bits stuck at the bottom.: When you add the finely grated fresh carrots , vanilla extract , and milk , pay attention to the batter consistency, which should be thick but scoopable. The grated carrots will distribute color and moisture, and the batter will smell brighter from the vanilla . Mixing thoroughly so there are no dry specks at the bottom is crucial, because unmixed pockets lead to dry, floury bites after microwaving. If the batter seems very stiff, add a tiny splash more milk , but too much will make the center undercooked. A common mistake is stopping when the top looks mixed while leaving dry bits at the base, so scrape the bottom well.
Microwave on high for 1 to 2 minutes (SEE NOTES). Top with whipped cream and more chopped pecans if desired.: As you fold the batter, listen for a slight change in texture and watch the batter cling smoothly to your spoon or fork. Ensuring the bottom is incorporated avoids uncooked streaks and promotes even rise. If you skip this, you may see dense streaks or flour pockets after cooking. A helpful trick is to press the batter into the mug's base and sides so it cooks uniformly. Expect a glossy sheen from the combined wet ingredients indicating readiness.
Microwave on high for 1 to 2 minutes (SEE NOTES).: The batter will transform from wet and glossy to a domed, soft cake; steam may escape from the surface and the aroma of cinnamon and brown sugar will intensify. Timing varies, so watch for the cake to rise and for the center to appear set rather than jiggly, though a slight spring is fine. If you overcook, the cake will dry out quickly, becoming tough instead of tender. For a safer approach, start at 1 minute and add 15 second bursts until done, especially with higher wattage microwaves. Avoid using metal and always place the mug on a microwave safe plate to catch any overflow.
Top with whipped cream and more chopped pecans if desired.: After the cake rests for a minute, the surface should be warm and fragrant, with tiny carrot flecks visible. Adding whipped cream introduces a cool creamy contrast and the extra chopped pecans restore crunch against the soft cake. If you add a topping immediately and it melts too much, let the cake cool slightly first to preserve texture. Resist adding cold toppings directly into a scalding cake, as they can collapse the structure and make slices look sloppy.