A notice figuring rather prominently on the façade of this mosque provides more information than I could find on the web: “[…] it was first built by Fatih Sultan Mehmed Khan and was given as a gift and granted to Sheıkh Muslihiddîn El-Hac Mustafa Ebu’l Vefâ Hazretleri who was one of the ulemas invited to Istanbul after the conquest in order to reconstruct t and guide the city.
[…] was once [a] külliye consisting of a mosque, madrasalı, Turkish bath, alms house, drinking fountain, cilehane and cells, it was ruined over time and there is now only a cilehane (place in which a dervish undergoes a period of trial and suffering) and a tomb. In 1913 it was utterly demolished with the aim of reparation, however, it could not be built for a long time. Eventually in 1994, it was built by the Mufti’s Office of Eminönü and Administration of Foundations and was opened to worship again.
The walls of the mosque are bonded with ashlar and bricks. Its roof is covered with a main dome, two half domes and a little half dome and the narthes is covered with five domes. Its mihrab, pulpit and rostrum are made of marble. “
The rest of the text describes the grave yard and its occupants.

The mosque is somewhat downhill from the Şehzade complex, approaching Süleymaniye. The district seems to be in for all sorts of renovations. The space inside the mosque I found very pleasing, some buildings “have it”. Must be them domes and half domes.