Connected Cars and their related technologies have been rapidly evolving in the last decade. One of the most crucial development areas addresses the aggregation of massive amounts of sensor data arriving continuously from a wide variety of hardware components: e.g. tyre sensors, cameras built on-board, and other external sources. Since the main aim of the manufacturers is to build safer, easier to drive, and more autonomous cars based on the collected data; they follow the latest ICT trends. Two technologies can be considered as already accepted and proven approaches at several application fields since they provide facilities (among others) to handle and process the generated, heterogeneous, large-scale, and rapidly growing data sets: Cloud computing and big data. The cloud infrastructure may act as an Internet of Things (IoT) backend, or as a kind of central hub by gathering the incoming sensor and other types of data. Moreover, the cloud offers elasticity in terms of data analytics and distribution services for such enormous amount of data. This paper details the second, private Platform-as-a-Service (PaaS) version of our cloud-oriented IoT back-end framework for Connected Cars and its scalable services relying on our experiences gained during the development of its first, Infrastructure-as-a-Service (IaaS) variant on an OpenNebula infrastructure. During the design and development stages we leveraged on the Cloud Foundry PaaS platform deployed at the premises of an automotive supplier company. The new reference implementation is able to handle, analyze and visualize vehicular data as illustrated by various use cases including Eco-driving, weather report/forecast, parameter coding over cloud, collection of CAN data, flashing devices remotely, etc.