Abstract We present results on the properties of extreme gas outflows in massive (M _* ∼ 10¹¹ M _⊙), compact, starburst (star formation rate, SFR∼ 200 M _⊙ yr⁻¹) galaxies at z = 0.4–0.7 with very high star formation surface densities (Σ_SFR ∼ 2000 M _⊙ yr⁻¹ kpc⁻²). Using optical Keck/HIRES spectroscopy of 14 HizEA starburst galaxies, we identify outflows with maximum velocities of 820–2860 km s⁻¹. High-resolution spectroscopy allows us to measure precise column densities and covering fractions as a function of outflow velocity and characterize the kinematics and structure of the cool gas outflow phase (T ∼ 10⁴ K). We find substantial variation in the absorption profiles, which likely reflects the complex morphology of inhomogeneously distributed, clumpy gas and the intricacy of the turbulent mixing layers between the cold and hot outflow phases. There is not a straightforward correlation between the bursts in the galaxies’ star formation histories and their wind absorption line profiles, as might naively be expected for starburst-driven winds. The lack of strong Mg ii absorption at the systemic velocity is likely an orientation effect, where the observations are down the axis of a blowout. We infer high mass outflow rates of ∼50–2200 M _⊙ yr⁻¹, assuming a fiducial outflow size of 5 kpc, and mass loading factors of η ∼ 5 for most of the sample. While these values have high uncertainties, they suggest that starburst galaxies are capable of ejecting very large amounts of cool gas that will substantially impact their future evolution.