A very similar dish is in the Harvard Art Museums/Arthur M. Sackler Museum, The Norma Jean Calderwood Collection of Islamic Art, inv. no. 2002.50.59. The Harvard museum website features a video demonstrating the interior of their dish as well as how it would have been constructed: http://www.harvardartmuseums.org/art/165023.
This style of construction, which includes seven circular compartments, must have been reserved for the celebration of 'Haft Sin' associated with the Persian New Year (Nowruz). Traditionally, seven items beginning with the letter 'sin' would be placed in each section, notably: sabzeh (wheat or barley, samanu (sweet pudding), senjed (dried olive), seer (garlic), seeb (apple), somaq (sumac) and serkeh (vinegar).