What is the optimal way to grind the Black Mushroom?
Since it was driving me mad that I didn't know what I was looking for (visually, that is), I took this screenshot of the black mushroom patch when I finally found it. Hope it helps:
I can also confirm that your character does not comment on the patch until clicking it.
It has several spawn points throughout Act I, but the most likely spawn point seems to be in Cathedral Level 1. It can spawn on all difficulties, and there's no difference between them, so you're best off blitzing through it on Normal. Your character will comment on the mushroom patch when you're in the room with it.
The best place to find Black Mushrooms is (as others have said) the Cathedral Level 1.
The Cathedral is randomly generated, so you'll want to explore Level 1 fully, and if you don't find it, leave the game and return. The Cathedral will regenerate, and you'll have another opportunity to find the mushroom.
If you've passed this area already, the best story checkpoint for this is "Act 1: Part 4 - Reign of the Skeleton King." You'll start in town, so use the waypoint in town to take you to the Cathedral Garden. Walk southwest, through the gate, and around to the front of the Cathedral. Open the door, and descend through the hole in the floor to get to Cathedral Level 1.
Arrowmaster also suggests starting with the quest "The Legacy of Cain," with the stage "Explore Cellar" - if you play through this quest to the checkpoint at the Cathedral, you'll shave a bit of time leaving and re-entering the game.