To improve the environmental implications of the growing demand of computing, future applications need to improve the carbon-efficiency of computing infrastructures. State-of-the-art approaches, however, do not consider the intermittent nature of renewable energy. The time and location-based carbon intensity of energy fueling computing has been ignored when determining how computation is carried out. This poses a new challenge -- deciding when and where to run applications across consumer devices at the edge and servers in the cloud. Such scheduling decisions become more complicated with the stochastic runtime variance and the amortization of the rising embodied emissions. This work proposes GreenScale, a framework to understand the design and optimization space of carbon-aware scheduling for green applications across the edge-cloud infrastructure. Based on the quantified carbon output of the infrastructure components, we demonstrate that optimizing for carbon, compared to performance and energy efficiency, yields unique scheduling solutions. Our evaluation with three representative categories of applications (i.e., AI, Game, and AR/VR) demonstrate that the carbon emissions of the applications can be reduced by up to 29.1% with the GreenScale. The analysis in this work further provides a detailed road map for edge-cloud application developers to build green applications.