This type of brushwasher is described as of 'gong-shape' or tangluo xi, as it has heavily compressed sides.
This washer belongs to an exclusive group of eight vessel shapes that are covered in this extremely desirable peachbloom glaze. Known as the ba da ma or 'Eight Great Numbers', the sets were especially devised in these classic forms to serve as requisite appointments for the Emperor's writing table. Complete sets are extremely rare, with one in the Metropolitan Museum of Art, New York, illustrated by S. Valenstein, The Handbook of Chinese Ceramics, New York, 1989 (rev. ed.), p. 237; and another from the Jingguantang Collection, sold in our Hong Kong rooms, 3 November 1996, lot 557.
Similar brushwashers have been widely published and are in numerous public and private collections. John Ayers in the transcript of his lecture, 'The 'Peachbloom' Wares of the Kangxi period (1662-1722)', TOCS, vol. 64, 1999-2000, pp. 31-50, provides a thorough discussion of peachbloom wares, as well as wares of similiar shape with pale celadon and pale blue glazes. He goes on to suggest p. 49, that these wares, rather than having been made exclusively for the use of the Kangxi emperor, may have also been presented as gifts to members of the court on important court occasions.
Whatever the case may be, these wares have always been and continue to be highly prized.