This is the Hekimoğlu Ali Paşa Mosque. He was the son (oğlu) of a court physician (hekim) and himself was Grand Vezir for 15 years under Sultan Mahmut I. The mosque dates from 1734-35, the architect was Ömer Ağa. It has characteristics of the classical style and of the new baroque style. It has tiles from the recently established Tekfur Saray kilns, rather than from the more traditional Iznik.

The mosque is one of my favorites, it's surrounded by a rather large garden, filled with cats that enjoy human kindness (and get that).