A little downhill from the Kariye museum there is this mosque, the Hoca Kasım Günani mosque. I found a site that says (I adjusted the English slightly):

"Address: Hobyar Mh. 34112 Fatih / Istanbul

Coordinate: 41.013193, 28.972939 Latitude: 41°0′47.49″N (41.013193)
Longitude: 28°58′22.58″E (28.972939)
Date Of Construction: 1558, Renovations: 1976

Built by: Hoca Kasım Günari

The construction of the mosque, which dates back to the period of Mehmet II, was by Hodja Kasim Gunani who was a schotar of his time. As is written on the tablet on the main gate, the mosque was restored in 1838. The mosque is known as Hasan Hüseyin Mascid after two men, named Hasan and Huseyin, who had been servants of Ebu Eyyup el-Ensari.

These men were buried here after they were martyred by being caught in this area while they were escapinq from the inconvenient behaviors [sic] of non-Muslims during their trip in the city allowed by the Rumelian Kaiser. The mosque was built in an ascending style and wooden. The inner part is 110 m² and the minbar, rostrum and mihrab are wooden white the inner sides of the walls are hand-worked. The place inside is also wooden.

While the minaret on the left side with one balcony is independent of the structure and with a pointed-tip, the outer side built with bricks was cemented. The wooden cover of the damaged mosque was renewed under the supervision of the foundations in 1970."

I was about to take pictures inside when I was ordered to leave by a woman who had the keys.