This paper advances the proactive eavesdropping research by considering a practical half-duplex mode for the legitimate monitor and dealing with the challenging case that the suspicious link opportunistically communicates over parallel fading channels. To increase eavesdropping success probability, we propose cognitive jamming for the monitor to change the suspicious link's long-term belief on the parallel channels' distributions, and thereby induce it to transmit more likely over a smaller subset of unjammed channels with a lower transmission rate. As the half-duplex monitor cannot eavesdrop the channel that it is simultaneously jamming to, our jamming design should also control the probability of such "own goal" that occurs when the suspicious link chooses one of the jammed (uneavesdroppable) channels to transmit. We formulate the optimal jamming design problem as a mixed integer nonlinear programming and show that it is non-convex. Nevertheless, we prove that the monitor should optimally use the maximum jamming power if it decides to jam, for maximally reducing suspicious link's communication rate and driving the suspicious link out of the jammed channels. Then we manage to simplify the MINLP to integer programming and reveal a fundamental trade-off in deciding the number of jammed channels: jamming more channels helps reduce the suspicious link's communication rate for overhearing more clearly, but increases own goal probability and thus decreases eavesdropping success probability. Finally, we extend our study to the two-way suspicious communication scenario, and show there is another interesting trade-off in deciding the common jammed channels for balancing bidirectional eavesdropping performances. Numerical results show that our optimized jamming-assisted eavesdropping scheme greatly increase eavesdropping success probability as compared with the conventional passive eavesdropping.