Harisa and haleem name closely related dishes found across a wide arc from the eastern Mediterranean through Iran, Central Asia and South Asia, built on the same basic method: whole grain, wheat or barley, is cooked for hours with meat, usually mutton, beef or chicken, until the grain breaks down and the meat shreds, producing a thick, smooth, porridge like dish traditionally beaten or pounded during cooking to help it break down further. The dish's long, slow cooking suits it to communal preparation for large gatherings, and it is that quality that ties it to two quite different religious settings recorded here honestly as two separate uses of one food rather than one meaning read into both.
In Shia Muslim communities marking Muharram, particularly the ten days leading to Ashura that commemorate the death of Husayn ibn Ali at Karbala, haleem is cooked in enormous batches at mosques and community halls and distributed free as nazr, a votive offering given in fulfillment of a vow or simply as charity, to anyone who comes, without regard to their means. Separately, and across a far wider range of Muslim communities not tied to Muharram at all, haleem and harisa are popular dishes for breaking the daily fast during Ramadan, valued simply because the dish is filling, warm and easy to prepare in quantity for a household or community iftar.