The species was first described scientifically by mycologists Melissa Danks, Teresa Lebel, and Karl Vernes in a 2010 issue of the journal Persoonia.

The specific epithet basorapulus is derived from the Latin words rapulum (a turnip) and baso (base) and refers to the distinct shape of the fruit bodies.

[3] The fruit body of Phlegmacium basorapulus is sequestrate, meaning that its spores are not forcibly discharged from the basidia, and it remains enclosed during all stages of development, including at maturity.

The outer skin of the cap (the pellis) is whitish to pale brown with a texture ranging from finely hairy to felt-like.

[2] Vegetation associated with the fungus includes Brachychiton populneus, Eucalyptus albens, E. elliptica, E. laevopinea and Exocarpus cupressiformis.