We present optical, radio, and X-ray observations of EP250108a/SN 2025kg, a broad-line Type Ic supernova (SN Ic-BL) accompanying an Einstein Probe (EP) fast X-ray transient at z = 0.176. EP250108a/SN 2025kg possesses a double-peaked optical light curve, and its spectrum transitions from a blue underlying continuum to a typical SN Ic-BL spectrum over time. We fit a radioactive decay model to the second peak of the optical light curve and find SN parameters that are consistent with the SN Ic-BL population, while its X-ray and radio properties are consistent with those of low-luminosity GRB (LLGRB) 060218/SN 2006aj. We explore three scenarios to understand the system’s multiwavelength emission: (a) SN ejecta interacting with an extended circumstellar medium (CSM), (b) the shocked cocoon of a collapsar-driven jet choked in its stellar envelope, and (c) the shocked cocoon of a collapsar-driven jet choked in an extended CSM. Models (b) and (c) can explain the optical light curve and are also consistent with the radio and X-ray observations. We favor model (c) because it can self-consistently explain both the X-ray prompt emission and first optical peak, but we do not rule out model (b). From the properties of the first peak in model (c), we find evidence that EP250108a/SN 2025kg interacts with an extended CSM and infer an envelope mass M_e ∼ 0.1 M_⊙ and radius R_e ∼ 4 × 10¹³ cm. EP250108a/SN 2025kg’s multiwavelength properties make it a close analog to LLGRB 060218/SN 2006aj and highlight the power of early follow-up observations in mapping the environments of massive stars prior to core collapse.