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Modern connected vehicles (CVs) frequently require diverse types of content for mission-critical decision-making and onboard users' entertainment. These contents are required to be fully delivered to the requester CVs within stringent deadlines that the existing radio access technology (RAT) solutions may fail to ensure. Motivated by the above consideration, this paper exploits content caching in vehicular edge networks (VENs) with a software-defined user-centric virtual cell (VC) based RAT solution for delivering the requested contents from a proximity edge server. Moreover, to capture the heterogeneous demands of the CVs, we introduce a preference-popularity tradeoff in their content request model. To that end, we formulate a joint optimization problem for content placement, CV scheduling, VC configuration, VC-CV association and radio resource allocation to minimize long-term content delivery delay. However, the joint problem is highly complex and cannot be solved efficiently in polynomial time. As such, we decompose the original problem into a cache placement problem and a content delivery delay minimization problem given the cache placement policy. We use deep reinforcement learning (DRL) as a learning solution for the first sub-problem. Furthermore, we transform the delay minimization problem into a priority-based weighted sum rate (WSR) maximization problem, which is solved leveraging maximum bipartite matching (MWBM) and a simple linear search algorithm. Our extensive simulation results demonstrate the effectiveness of the proposed method compared to existing baselines in terms of cache hit ratio (CHR), deadline violation and content delivery delay.