Battarrea? Found in northern New Mexico, USA in Pinon-Juniper woodlands at 7000 ft asl. The cross-hatched area is the part that was below ground. I think what appears to be a cap is actually the bottom half of a puffball that has fallen down. Spores are rust colored. Placed on 8.5 x 11" paper for scale.
Take a look at these close-ups. The whitish "underside" is smooth, the top is kinda hairy (and where the spores are).
Stem sure looks like a Tulostoma. Do you think the thin layer (Pellicle) on the cap has come off (disintegrated) with age, revealing just the spore mass (spores at various states of maturity)? were you able to find several at different stages of maturity?
Yes, I think the cap has come off. If I have a chance this afternoon, I'll go back and look for other specimens.
One difference between this specimen and photos of Tulostoma on the internets is that 5" of this one was underground.
there were about 100 species of Tulostoma described in the 1920's, most from the SouthWest. I'll check some books to see if any have buried stems.
Others nearby (from 3" to 3' away from original). None as tall as the original (purslane provides some scale) In the first one here, it looks like the bottom half of the ball has fallen away.
Just checked the books, your specimen closely matches the genus Battarrea. "lacerate woody stalk which arises below ground from a woody volva" and "some Mexican species have a stalk of 65 cm". Also states that the gleba is often naked (i.e. no covering of the spore mass at maturity).
Battarrea phalloides seems likely (looking at "Mushrooms and Truffles of the Southwest/Jack S. States"