Minecraft – Can you grow a Giant Mushroom by planting a mushroom in the Giant Mushroom biome

When Minecraft 1.2 is released, using the new “Anvil” file format, biomes will be stored in the chunk data so that they can be redefined on a per-column (x,z) basis. You will need an editor which supports doing so, or a generic NBT editor, of course. (Source)

You used to be able to plant mushrooms on any surface, then make them grow into Huge Mushrooms using Bone Meal. This would, for some reason, convert the tile below the mushroom's stipe to dirt.

This was obviously a bug (as it would allow players to, for example, destroy Bedrock), and was fixed at some point. So no, this is no longer possible.