Nowadays, Unmanned Aerial Vehicles (UAVs) represent a significant aid on scenarios where fixed, ground infrastructures are temporarily or permanently not available; this is the case of large-scale applications of the Internet of Things (IoTs), e.g. smart city and agriculture 3.0, where the UAVs can be employed as mobile data mules and gather the data from Wireless Ground Sensors (WGSs). UAV-aided wireless sensor networks (WSNs) introduce considerable advantages both in terms of performance and costs since they avoid the need of error-prone multi-hop communications, and also the installation of static gateways; at the same time, they pose formidable research challenges for their implementation, like the synchronization issue between the UAV and the WGS and the path planning, which should take into account the extremely limited flight autonomy of the UAVs. In this paper, we address both the issues above by proposing BEE-DRONES, a novel framework for large-scale, ultra low-power UAV-aided WSNs. In order to mitigate the synchronization problem, we investigate the utilization of passive Wake-up Radio (WR) technology on the WGSs, and of wireless power transfer from the UAVs: by harvesting the energy from the UAV hovering over it, the WGS is activated only for the short time required to transfer the data toward the mobile sink, while it experiences zero-consumption in sleep mode. We investigate the performance of passive WR-based WGS through real measurements, under different WGS-UAV distances and antenna orientations. Then, based on such results, we formulate the joint WGS scheduling and UAV path planning problem, where the goal is to determine the optimal trajectory of the UAVs activating the WR-based WGSs while taking into account the Value of the Sensing (VoS) as well as the total lifetime of the WSN. The original problem is transformed into a multi-commodity flow problem, and both centralized and distributed heuristics over the multi-graph are proposed. Finally, we evaluate the proposed algorithms through extensive OMNeT++ simulations; the results demonstrate the gain of BEE-DRONES in terms of extended lifetime compared to traditional, non WR-based solutions (e.g. duty-cycle), and in terms of reduced data-correlation compared to non VoS-aware path planning solutions.