Hed paw - a source of admiration, pollution, and naming confusion

On the plane from Bangkok to Chiang Mai yesterday, I sat next to a friendly American expat, Craig, who mentioned that the hill tribe people do semi-controlled burns that have something to do with mushroom collecting. He googled it on his phone before takeoff, and confirmed that the burns are set to facilitate the collection of "hed paw/hed tawp," some sort of semi-buried mushroom that isn't cultivated and can be sold for high prices (source). While these mushrooms are highly sought after, the unpopular burns conducted to find them are blamed for some of the air pollution in the area.

Mature Astraeus sp.

Based on this initial description, I expect these fungi are mycorrhizal (hence practically impossible or economically unfeasible to cultivate). The brief and vague description reminded me of morels, which are mycorrhizal, not commercially cultivated, expensive, and are found in great numbers after fires. I asked Keith, the friendly British expat guesthouse proprietor, if he was familiar with any of the mushrooms sold locally, and he spoke highly of some sort of brown, round, lumpy mushroom, sometimes called the Chiang Mai truffle. He said they are very seasonal (suggesting that they aren't cultivated), and I expect that these brown lumps are the "hed paw" mushroom.

Immature Astraeus sp. - when they are eaten

After a bit more googling, it looks like the mushroom is a "false earthstar" (Astraeus spp.), a widely found genus of mycorrhizal fungi. One source that discussed the mushroom in the context of the slash-and-burn approach of the hill tribes called it Astraeus hygrometricus, though this name was given to most similar Astraeus species globally and represented a species complex until the early 2000s. According to Wikipedia, molecular and morphological evidence indicates that Thai Astraeus species previous lumped under the name A. hygrometricus include Astraeus asiaticus Phosri, M.P.Martín & Watling (2007) and Astraeus odoratus Phosri, Watling, M.P.Martín & Whalley (2004) syn. thailandicus Petcharat (2003). There is some uncertainty about whether the burns are set to clear the underbrush and make the mushrooms easily visible or if the fire itself triggers a flush of fruiting, as with morel species. For more info, one of the Wiki sources (a 2004 Mycotaxon pub, "The genus Astraeus in Thailand") is free access. The excellent Cornell mycology  blog also did a post about Astraeus species in North America v. ones in Thailand very recently that does a better job of describing the problem with naming within the Astraeus genus.

Interior endoperidium brown with spores forming; exoperidium splits into a star shape when mature, and lifts endoperidium above leaf litter to eject spores.

I trotted downstairs and asked Keith if the image on the Cornell blog matched the mushroom he was fond of, and he confirmed that it did. Raitree, a Thai woman and the other proprietor of the guesthouse, quickly named it in Thai -- "hed paw" indeed. She then called one of her friends who said the season ended two months ago in May, but I'm still going to keep my eyes peeled for brown lumps (and other mushrooms) at the Sunday market.

UPDATE- 9/8, found some Astraeus sp. (tentatively ID-ed, pictured above) in Ban Tak. A local called it "het thawp," suggesting it is the species that they consume when immature.