This is the Zal Mahmut Paşa mosque, dating from 1577.
The Strolling through Istanbul guide has it the Zal Mahmut Paşa mosque is the "grandest and most interesting mosque in Eyüp, a mature but unique work of Sinan." Zal "was a rather unsavoury character, when in 1553 Süleyman had his son Mustafa put to death, it was Mahmut (who got his forename Zal from that of a Persian hero famous for his Herculean strength) who overcame the young prince’s resistance and strangled him. Later he married the Princess Şah Sultan, sister of Selim the Sot, as a reward, it is said for having smoothed that prince’s path to the throne by the elimination of his brother. In 1580 Zal and his wife died in a single night.