The cake is the yeast. Cold crash to get it all to drop, then decant off the beer and add some boiled/cooled water. The yeast settles on top of the trub for the most part, so you can carefully swirl to get some of the top stuff off without getting the trub suspended.
I don't usually wash my yeast and have never had problems. I don't leave as much beer as you, in fact I'll decant all the beer I can off the cake then use a clean ladle to fill a 1-cup jar and save that in the fridge for up to several months. I can use it direct for the firt month, or make a starter later.