The IceCube Neutrino Observatory utilizes the Cherenkov radiation emitted by charged secondary particles produced in interactions of neutrinos with ice nucleons to detect neutrino events. “Starting events”, where this interaction vertex is contained inside the detector volume, can be used to distinguish neutrinos from the dominant background of atmospheric through-going muons. We present the Medium Energy Starting Events (MESE) selection, which employs a series of vetoes to obtain a neutrino-pure sample to measure the flux of diffuse extragalactic neutrinos from 1~TeV to 10~PeV from the entire sky. In this talk we will present a measurement of the spectrum of the diffuse flux of neutrinos, which demonstrates strong evidence for structure in the spectrum beyond a single power law, with a significance of $4.2\,\sigma$.