Coronal jets are short-lived eruptive features commonly observed in polar coronal holes and are thought to play a key role in the transfer of mass and energy into the solar corona. We describe unique contemporaneous observations of a coronal blowout jet seen by the Extreme Ultraviolet Imager onboard the Solar Orbiter spacecraft (SO/EUI) and the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO/AIA). The coronal jet erupted from the south polar coronal hole, and was observed with high spatial and temporal resolution by both instruments. This enabled identification of the different stages of a breakout reconnection process producing the observed jet. We find bulk plasma flow kinematics of ∼100–200 km s−1 across the lifetime of its observed propagation, with a distinct kink in the jet where it impacted and was subsequently guided by a nearby polar plume. We also identify a faint faster feature ahead of the bulk plasma motion propagating with a velocity of ∼715 km s−1 which we attribute to untwisting of newly reconnected field lines during the eruption. A Differential Emission Measure (DEM) analysis using the SDO/AIA observations revealed a very weak jet signal, indicating that the erupting material was likely much cooler than the coronal passbands used to derive the DEM. This is consistent with the very bright appearance of the jet in the Lyman-α passband observed by SO/EUI. The DEM was used to estimate the radiative thermal energy of the source region of the coronal jet, finding a value of ∼ 2 × 1024 ergs, comparable to the energy of a nanoflare.