The distribution of spacecraft in the inner heliosphere during 2019 March enabled comprehensive observations of an interplanetary coronal mass ejection (ICME) that encountered Parker Solar Probe (PSP) at 0.547 au from the Sun. This ICME originated as a slow (∼311 km s-1) streamer blowout (SBO) on the Sun as measured by the white-light coronagraphs on board the Solar TErrestrial RElations Observatory-A and the Solar and Heliospheric Observatory. Despite its low initial speed, the passage of the ICME at PSP was preceded by an anisotropic, energetic (≲100 keV/n) ion enhancement and by two interplanetary shocks. The ICME was embedded between slow (∼300 km s-1) solar wind and a following, relatively high-speed (∼500 km s-1), stream that most likely was responsible for the unexpectedly short (based on the SBO speed) ICME transit time of less than ∼56 hr between the Sun and PSP, and for the formation of the preceding shocks. By assuming a graduated cylindrical shell (GCS) model for the SBO that expands self-similarly with time, we estimate the propagation direction and morphology of the SBO near the Sun. We reconstruct the flux-rope structure of the in situ ICME assuming an elliptic-cylindrical topology and compare it with the portion of the 3D flux-rope GCS morphology intercepted by PSP. ADAPT-WSA-ENLIL-Cone magnetohydrodynamic simulations are used to illustrate the ICME propagation in a structured background solar wind and estimate the time when PSP established magnetic connection with the compressed region that formed in front of the ICME. This time is consistent with the arrival at PSP of energetic particles accelerated upstream of the ICME.