Earth observation (EO) data volumes are rapidly increasing. While cloud computing are now used for processing large EO datasets, the energy efficiency aspects of such a processing have received much less attention. This issue is notable given the increasing awareness of energy costs and carbon footprint in big data processing, particularly with increased attention on compute-intensive foundation models. In this paper we identify gaps in energy efficiency practices within cloud-based EO big data (EOBD) processing and propose several research directions for improvement. We first examine the current EOBD landscape, focus on the requirements that necessitate cloud-based processing and analyze existing cloud-based EOBD solutions. We then investigate energy efficiency strategies that have been successfully employed in well-studied big data domains. Through this analysis, we identify several critical gaps in existing EOBD processing platforms, which primarily focus on data accessibility and computational feasibility, instead of energy efficiency. These gaps include insufficient energy monitoring mechanisms, lack of energy awareness in data management, inadequate implementation of energy-aware resource allocation and lack of energy efficiency criteria on task scheduling. Based on these findings, we propose the development of energy-aware performance monitoring and benchmarking frameworks, the use of optimization techniques for infrastructure orchestration, and of energy-efficient task scheduling approaches for distributed cloud-based EOBD processing frameworks. These proposed approaches aim to foster more energy awareness in EOBD processing , potentially reducing power consumption and environmental impact while maintaining or minimally impacting processing performance.