Hydnoplicata convoluta

The fruit body is stemless, dry, fleshy and convolutedly folded (hence somewhat brain-like, as shown here: https://www.anbg.gov.au/fungi/images-captions/peziza-whitei-0085.html). The fruitbodies may grow to about 3 centimetres in maximum dimension and are creamy to pale brown. The convoluted structure is shown well in this cross-section:  https://www.anbg.gov.au/fungi/images-captions/peziza-whitei-0086.html.

The folds are fairly loose and the fruitbody is somewhat fragile so that the fruitbody may show cracks or have broken bits. The fruitbodies are found on soil in a wide variety of wooded habitats.

This is a native species and the first published description (as Hydnocystis convoluta) appeared in 1895, with various names since then (including Peziza whitei for many years). The paper listed below gives the details and more information.

Look-alikes

This species is fairly distinctive. Some of the large cup-like fruiting bodies of Peziza (with similar colouring) may become distorted, but never in such a folded way as to obliterate the basic cup-like form. A Gyromitra fruitbody consists of a convolutedly folded 'head' atop a stem. At least some species of Genea, Geopora, Gilkeya, Gymnohydnotrya and Hydnotrya have convolutedly folded fruitbodies and are found on soil, but seem to be robust or with non-smooth surfaces. Of those five, Genea, Gymnohydnotrya and Geopora have been reported from Australia.  

Various brain-like fungi occur on wood and cyanobacteria of the genus Nostoc are convoluted and grow on soil. However, those are gelatinous when fresh, hard when dry and those of Nostoc are dark greenish.

Reference

J.M. Trappe & A.W. Claridge, 2006, Australasian sequestrate fungi 17: The genus Hydnoplicata (Ascomycota, Pezizaceae) resurrected, Australasian Mycologist, 25, 33-36. Available at: https://www.australasianmycologicalsociety.com/volume-251.