Cook the yam or sweet potato in boiling water until soft, but not mushy.
Peel, cut in 1/2-inch slices, and reserve.
To make the cebiche, start by cutting the onion (the thinner the better), and soaking it in very cold water (if possible, with ice), for about 10 minutes. This will help remove the sharpness of the raw onion.
Place the mushrooms in a colander and pour boiling water over them. Drain well and transfer to a bowl.
Drain and add the onion to the bowl with all the other ingredients, except the yam or sweet potato.
Let marinate for 10 minutes.
Serve with a few slices of yam or sweet potato on the side. You can also serve over a lettuce leaf, with boiled giant kernel corn on the side.