I guess this is the "honeycombed entrance" to the Khanqah al-Farafra, "a rare example of a Muslim (Sufi) monastery. The rather severe but pleasing building was constructed in 1237 in the name of the Ayyubid Governor, al-Nasr Yusuf II, son of Sultan al-Aziz (was Ayyubid governor of Aleppo, 1216-36), but probably actually endowed by his mother. Note the honeycombed entrance, the large Iwan in the courtyard [...], cells surround the courtyard. Next door to the east is the headquarters of the Office for the Protection of Old Aleppo. "

I am not certain though. I entered the building next door, which gave me much more of a feel of being in a former monastery. It may be the entrance to that complex has shifted. See next pictures.