The most appropriate explanation for the brown solids present in the bottom of the mug is:
The cocoa was mixed with hot water, but some cocoa settled as it cooled because the solubility went down.
As the hot cocoa cools, the solubility of cocoa powder decreases, causing some of the dissolved cocoa to precipitate out as solids. This is a common phenomenon in solutions where temperature decreases, resulting in the reduction of solubility for some substances.