This is the Nişancı Mehmet Paşa mosque, according to the Strolling Through Istanbul guide NOT by Sinan, but some unknown architect. It dates from 1584-88 and was built for the Keeper of the Seal (Nişancı) Mehmet Paşa.
I came across it a couple of years back and when I am near always visit it, because it is a fine building, sitting in a nice garden in a curious neighbourhood.