Over-the-Air (OTA) software updates are becoming essential for electric/electronic vehicle architectures in order to reduce recalls amid the increasing software bugs and vulnerabilities. Current OTA update architectures rely heavily on direct cellular repository-to-vehicle links, which makes the repository a communication bottleneck, and increases the cellular bandwidth utilization cost as well as the software download latency. In this paper, we introduce ScalOTA, an end-to-end scalable OTA software update architecture and secure protocol for modern vehicles. For the first time, we propose using a network of update stations, as part of Electric Vehicle charging stations, to boost the download speed through these stations, and reduce the cellular bandwidth overhead significantly. Our formalized OTA update protocol ensures proven end-to-end chain-of-trust including all stakeholders: manufacturer, suppliers, update stations, and all layers of in-vehicle Electric Control Units (ECUs). The empirical evaluation shows that ScalOTA reduces the bandwidth utilization and download latency up to an order of magnitude compared with current OTA update systems.