We provide analysis of a coronal mass ejection (CME) that passed over Parker Solar Probe (PSP) on January 20, 2020 when the spacecraft was at just 0.32 AU. The Integrated Science Investigation of the Sun instrument suite measures energetic particle populations associated with the CME before, during, and after its passage over the spacecraft. We observe a complex evolution of energetic particles, including a brief ~2 h period where the energetic particle fluxes are enhanced and the nominal orientation of the energetic particle streaming outward from the Sun (from 30 to 100 keV nuc −1 ) abruptly reverses inward toward the Sun. This transient and punctuated evolution highlights the importance of magnetic field structures that connect the spacecraft to different acceleration sites, one of which is likely more distant from the Sun than PSP during the evolution of the CME. We discuss these characteristics and what they tell us about the source of the energetic particles. During this period, PSP was radially aligned with the Solar Terrestrial Relations Observatory A (STEREO-A), which measured the same CME when it passed 1 AU. The magnetic field measurements at both spacecraft are remarkably similar, indicating that the spacecraft are likely encountering the same portion of the magnetic structure that has not evolved significantly in transit. The energetic particle observations on the other hand, are quite different at STEREO-A, showing how transport effects have acted on the energetic particle populations and obscured the detailed properties present earlier in the development of the CME. This event provides a unique case study in how energetic particle populations evolve as CMEs propagate through the heliosphere.