Start by grabbing a microwave-safe mug. Add the flour, baking powder, sugar, and a small pinch of salt directly into the mug. Use a fork or small whisk to stir everything together until the dry ingredients are evenly blended and there are no clumps.
Next, pour in the melted butter, milk, and vanilla extract. Stir the mixture well, scraping along the bottom and sides of the mug to make sure all the flour is fully mixed in.
Keep stirring until the batter looks smooth and there are no dry spots left. Add the sprinkles and gently fold them into the batter. Mix just enough to spread them through evenly.
The batter should be smooth and slightly thick, but not overworked. Place the mug in the microwave and cook on high for 1 to 2 minutes. Start with 1 minute, then check the cake.
The top should look set and feel slightly springy when you touch it lightly. If needed, microwave for a few more seconds. Let the cake cool for about a minute before eating.