The flux of high-energy neutrinos passing through the Earth is attenuated due to their interactions with matter. The interaction rate is modulated by the neutrino interaction cross section and affects the flux arriving at the IceCube Neutrino Observatory, a cubic-kilometer neutrino detector embedded in the Antarctic ice sheet. We present a measurement of the neutrino cross section between 60 TeV and 10 PeV using the high-energy starting events (HESE) sample from IceCube with 7.5 years of data. The result is binned in neutrino energy and obtained using both Bayesian and frequentist statistics. We find it compatible with predictions from the Standard Model. Flavor information is explicitly included through updated morphology classifiers, proxies for the the three neutrino flavors. This is the first such measurement to use the three morphologies as observables and the first to account for neutrinos from tau decay.