This is the Hussein Agha Mosque, at (probably) nr. 48. An article I found concerning its restoration has "The Hüseyin Ağa Mosque, which dates back to the end of the 16th century is a sweet little place with its Kutahya tiles, calligraphy, colored glass windows and floors covered with İsparta rugs. It will look even better when the long-awaited restoration project is completed. But as for who Galatasaray Ağası Seyhulharem Hüseyin Ağa - who had the mosque built, probably in 1596 (1005 A.H.), although it might actually have been built in 1591 or 1594 – was, there is no agreement. And why build it in a place in an undeveloped part of Istanbul, even outside the walls?
Beyoğlu attracted foreigners, as the old embassies - now consulates - along Istiklal Caddesi attest. There were also numerous Christian churches of one denomination or another, but Ağa Camii is the only Muslim mosque along the entire length of the street and that is perhaps why it was built. The Taksim area in 1596 would still have been sparsely inhabited, open countryside. It would be more than a hundred years later that the water distribution center that gives today’s square its name would be built, and more than two hundred years later before a military barracks would replace the cemeteries that had grown outside the city limits."