Mix together 1 tablespoon + 2 teaspoons of milk and the vinegar in a microwave safe mug. Let sit for 3-4 minutes.
Mix in the remaining cake ingredients (including the other 1 tablespoon of milk) until fully combined.
Microwave for around 1 minute, and let stand for around 15 minutes to allow cake to cool.
In a small bowl, mix together the cream cheese frosting ingredients until smooth. Frost the cooled mug cake, and top with sprinkles!