In a large coffee cup (12 ounces or larger), stir together the flour, sugar, baking powder and salt.
Add the melted butter, egg yolk, milk and vanilla extract. Stir until it forms a thick cake batter. Stir in the sprinkles. Scrape down the sides.
Microwave for 70-80 seconds. If it still looks doughy, microwave in 10 seconds intervals. Microwaves and the width of mugs vary greatly, so it can take some time to get the right amount.
Remove and allow to cool slightly before frosting.
To Make Frosting:
In a small bowl, combine the butter and powdered sugar until smooth. Add the milk and vanilla. Use a drop of food coloring, if desired.
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