Vehicular Edge Computing (VEC) has emerged as a promising paradigm to enable low-latency Vehicle-to-Everything (V2X) services by bringing computing resources closer to vehicles. However, the high dynamicity of vehicular networks poses significant challenges in designing an optimal policy for delivering V2X services while ensuring security and timely service delivery. To address these challenges, this paper proposes a BlockchainEnabled Vehicular Edge Computing (BEVEC) framework that employs a dual-layer verification process empowered with a permissioned blockchain to ensure data accuracy and integrity. A novel system utility function is designed to measure the performance of the BEVEC, which also serves as the basis for a consensus mechanism of the permissioned blockchain. To optimize this utility, a Deep Reinforcement Learning (DRL) algorithm is proposed to enable timely service delivery in BEVEC. Simulation-based results demonstrate the effectiveness of the proposed algorithm when compared to existing approaches. On average, it obtained an 18% reduction in latency, a 38% improvement in successful service delivery, and a 65% decrease in energy consumption.