Black ash buildup occurs when there's a high level of sulfur being emitted. Sadly, the only way to fix this issue is to have all affected drywall replaced. If you only smell rotten eggs when hot ...

Hydrogen sulfide gas causes the "rotten-egg" or sulfur water smell ... The corrosion of iron and steel from sulfur forms ferrous sulfide or "black water." Hydrogen sulfide in water can blacken ...