The utility of the object can only be guessed at. If the only holes are around the rim with none elsewhere suggests a use as a liquid measuring or liquid separation device. Possibly for industrial rather than domestic use, perhaps dairy or cheese making but the decoration suggests home usage?
The body may be ironstone with the faux marble decoration under the glaze. DAVENPORT did have at least two printed marble patterns. Are there any marks suggesting print application rather stick or brush application of the blue.
The base shows an impressed potting date of 1858 which actually includes 1859 too.