Place butter in a large mug and microwave 30 to 40 seconds until melted. Allow to cool 2 to 3 minutes.
Quickly whisk in the milk, vanilla extract, and sugar, mixing well (if the butter begins to solidify, microwave it for 30-45 seconds to warm the milk). Whisk in the flour, baking powder, and salt until combined. Stir in the sprinkles.
Microwave for 80 to 90 seconds. The top should look set but slightly wet when done. Cool a few minutes before enjoying.
Notes
Make ahead: You can prepare this mug cake in advance, cover with plastic wrap and store for up to 2 days at room temperature.