A couple of thoughts....
I was reading the reviews, and it sounds like you'd have some sauce from the compote if you don't reduce it as much as the recipe calls for. You could thicken it a bit with arrowroot or cornstarch, if that is what you are looking for.
Another possibility would be a sort of chimichurri sauce.
I made the one from the updated Joy of Cooking, using cilantro and it was a hit. If cilantro isn't to your liking, then parsley would be fine.
Let us know how it turns out. I love shiitake muchrooms.