CeSiI has been recently isolated in the ultrathin limit, establishing CeSiI as the first intrinsic two-dimensional van der Waals heavy-fermion material up to 85 K. We show that, due to the strong spin−orbit coupling, the local moments develop a multipolar real-space magnetic texture, leading to local pseudospins with a nearly vanishing net moment. To elucidate its Kondoscreened regime, we extract from first-principles the parameters of the Kondo lattice model describing this material. We develop a pseudofermion methodology in combination with ab initio calculations to reveal the nature of the heavy-fermion state in CeSiI. We analyze the competing magnetic interactions leading to an unconventional heavy-fermion order as a function of the magnetic exchange between the localized f-electrons and the strength of the Kondo coupling. Our results show that the magnetic exchange interactions promote an unconventional momentumdependent Kondo-screened phase, establishing the nature of the heavy-fermion state observed in CeSiI.