In intelligent transportation systems (ITS), vehicles are expected to feature with advanced applications and services which demand ultra-high data rates and low-latency communications. For that, the millimeter wave (mmWave) communication has been emerging as a very promising solution. However, incorporating the mmWave into ITS is particularly challenging due to the high mobility of vehicles and the inherent sensitivity of mmWave beams to dynamic blockages. This article addresses these problems by developing an optimal beam association framework for mmWave vehicular networks under high mobility. Specifically, we use the semi-Markov decision process to capture the dynamics and uncertainty of the environment. The Q-learning algorithm is then often used to find the optimal policy. However, Q-learning is notorious for its slow-convergence. Instead of adopting deep reinforcement learning structures (like most works in the literature), we leverage the fact that there are usually multiple vehicles on the road to speed up the learning process. To that end, we develop a lightweight yet very effective parallel Q-learning algorithm to quickly obtain the optimal policy by simultaneously learning from various vehicles. Extensive simulations demonstrate that our proposed solution can increase the data rate by 47% and reduce the disconnection probability by 29% compared to other solutions.