The correct explanation for the brown solids at 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.
When hot cocoa is prepared, more cocoa powder can dissolve in hot water due to increased solubility at higher temperatures. As the cocoa cools, its solubility decreases, causing some of the dissolved cocoa to come out of solution and settle at the bottom of the mug.