Distributed digital infrastructures for computation and analytics are now evolving towards an interconnected ecosystem allowing complex applications to be executed from IoT Edge devices to the HPC Cloud (aka the Computing Continuum, the Digital Continuum, or the Transcontinuum). Understanding end-to-end performance in such a complex continuum is challenging. This breaks down to reconciling many, typically contradicting application requirements and constraints with low-level infrastructure design choices. One important challenge is to accurately reproduce relevant behaviors of a given application workflow and representative settings of the physical infrastructure underlying this complex continuum. We introduce a rigorous methodology for such a process and validate it through E2Clab. It is the first platform to support the complete experimental cycle across the Computing Continuum: deployment, analysis, optimization. Preliminary results with real-life use cases show that E2Clab allows one to understand and improve performance, by correlating it to the parameter settings, the resource usage and the specifics of the underlying infrastructure.