We report on our study of supernova (SN) 2022xxf based on observations obtained during the first four months of its evolution. The light curves (LCs) display two humps of similar maximum brightness separated by 75 days, unprecedented for a broad-lined (BL) Type Ic supernova (SN IcBL). SN 2022xxf is the most nearby SN IcBL to date (in NGC 3705, $z = 0.0037$, at a distance of about 20 Mpc). Optical and near-infrared photometry and spectroscopy are used to identify the energy source powering the LC. Nearly 50 epochs of high signal-to-noise-ratio spectroscopy were obtained within 130 days, comprising an unparalleled dataset for a SN IcBL, and one of the best-sampled SN datasets to date. The global spectral appearance and evolution of SN 2022xxf points to typical SN Ic/IcBL, with broad features (up to $sim14000$ km s$^{-1}$) and a gradual transition from the photospheric to the nebular phase. However, narrow emission lines (corresponding to $sim1000-2500$ km s$^{-1}$) are present in the spectra from the time of the second rise, suggesting slower-moving circumstellar material (CSM). These lines are subtle, in comparison to the typical strong narrow lines of CSM-interacting SNe, for example, Type IIn, Ibn, and Icn, but some are readily noticeable at late times such as in Mg I $lambda$5170 and [O I] $lambda$5577. Unusually, the near-infrared spectra show narrow line peaks in a number of features formed by ions of O and Mg. We infer the presence of CSM that is free of H and He. We propose that the radiative energy from the ejecta-CSM interaction is a plausible explanation for the second LC hump. This interaction scenario is supported by the color evolution, which progresses to the blue as the light curve evolves along the second hump, and the slow second rise and subsequent rapid LC drop. (Abstract abridged)