This is a rare buckwheat endemic to sandstone outcrops in the central Santa Lucia Mountains. It's a small, suffrutescent, subshrub which has lots of small, pale-green, narrowly-elliptic leaves with margins revolute and whitish tomentum conspicuous above and (much more densely) below. The portions of the stems below the foliage have a densely ringed & rumpled appearance formed by the attachment scars from past years fallen leaves. The flowers appear in solitary involucres at the tips of abundant inflorescence branches. Perianths are monomorphic (= lobes of equal size & shape) and mostly ochroleucous...with red mid-lines on the backs of the lobes, and a deeper yellow at the perianth base.

Originally described in 1961 by J. T. Howell based on material collected in 1960 by the renowned Monterey botanist Clare Butterworth Hardham, it was named (according to Jim Reveal's June 15, 1987 field notes) for both her and her father, the latter having died in 1961. The following is from an obituary in the November 2010 Monterey CNPS chapter newsletter:

'Clare Butterworth Hardham (1918-2010), wife of John Fraser Hardham. Her field work on the central and south coasts and the Santa Lucia Mountains was legendary; she had a number of special plants named for her, including the rare/endangered Pogogyne hardhamiae, Eriogonum butterworthianum and Galium hardhamiae, all of which are found in Monterey County. She is the plant name author of Collinsia antonina which she found near Fort Hunter Liggett. Born and raised on the family ranch in Santa Barbara, she earned a B.A. from Vassar College and an M.S. at U.C. Santa Barbara. With her husband, John F. Hardham, M.D., she had three children, Ann, Virginia and John; and operated a cattle ranch raising polled Herefords for many years.'

Further info can be found at these links: Reveal(1989), FNA species description, ESCPT species fact sheet, and CNPS Rare Plant Inventory species page.

I'd been hoping to see this in flower for more than 15 years, and it was a delight to behold & study.