Existing portrait relighting methods struggle with precise control over facial shadows, particularly when faced with challenges such as handling hard shadows from directional light sources or adjusting shadows while remaining in harmony with existing lighting conditions. In many situations, completely altering input lighting is undesirable for portrait retouching applications: one may want to preserve some authenticity in the captured environment. Existing shadow editing methods typically restrict their application to just the facial region and often offer limited lighting control options, such as shadow softening or rotation. In this paper, we introduce COMPOSE: a novel shadow editing pipeline for human portraits, offering precise control over shadow attributes such as shape, intensity, and position, all while preserving the original environmental illumination of the portrait. This level of disentanglement and controllability is obtained thanks to a novel decomposition of the environment map representation into ambient light and an editable gaussian dominant light source. COMPOSE is a four-stage pipeline that consists of light estimation and editing, light diffusion, shadow synthesis, and finally shadow editing. We define facial shadows as the result of a dominant light source, encoded using our novel gaussian environment map representation. Utilizing an OLAT dataset, we have trained models to: (1) predict this light source representation from images, and (2) generate realistic shadows using this representation. We also demonstrate comprehensive and intuitive shadow editing with our pipeline. Through extensive quantitative and qualitative evaluations, we have demonstrated the robust capability of our system in shadow editing.