Mirimiran Ağa türbesi is almost opposite the Sokullu Mehmet Paşa one. I found texts referring to the man’s career, from which I gather he served under Sultan III Murad (1574-1595), as well as Sultan Selim (1566-1574) and was a vizier in 1587. For reasons connected with the Janissaries Mehmed Agha was executed in 1589.
I found no information regarding the architect, the türbe caries 1589 as a date.