The inherent dynamism of recent technological advancements in intelligent vehicles has seen multitudes of noteworthy security concerns regarding interactions and data. As future mobility embraces the concept of vehicles-to-everything, it exacerbates security complexities and challenges concerning dynamism, adaptiveness, and self-awareness. It calls for a transition from security measures relying on static approaches and implementations. Therefore, to address this transition, this work proposes a hierarchical self-aware security architecture that effectively establishes accountability at the system level and further illustrates why such a proposed security architecture is relevant to intelligent vehicles. The article provides (1) a comprehensive understanding of the self-aware security concept, with emphasis on its hierarchical security architecture that enables system-level accountability, and (2) a deep dive into each layer supported by algorithms and a security-specific in-vehicle black box with external virtual security operation center (VSOC) interactions. In contrast to the present in-vehicle security measures, this architecture introduces characteristics and properties that enact self-awareness through system-level accountability. It implements hierarchical layers that enable real-time monitoring, analysis, decision-making, and in-vehicle and remote site integration regarding security-related decisions and activities.