Existing emotional support conversation (ESC) systems mainly rely on end-to-end response generation or coarse strategy supervision, offering limited interpretability and little support for systematic skill improvement. We propose ESC-Skills, a skill-centric framework that discovers and self-evolves executable emotional support skills. We first model localized support interactions as Intervention Units (IUs), which capture state--action--outcome dynamics between seeker states, support interventions, and post-response emotional changes. Based on IUs extracted from both successful and failed ESC dialogues, we construct the ESC-Skills Bank, a repository of executable emotional support skills containing intervention guidance, applicability conditions, expected outcomes, and potential risks. To further improve robustness, we introduce a multi-profile self-evolutionary refinement framework in which an ESC agent interacts with diverse simulated seeker profiles under SAGE evaluation. The resulting interaction traces are analyzed to identify missing skills, unsafe interventions, and profile-specific failure patterns, which are then used to refine the Skills Bank through simulation-based verification. Experimental results demonstrate that ESC-Skills improves both response-level quality and dialogue-level emotional outcomes while providing more interpretable and controllable support behaviors. We will release the code, prompts, and ESC-Skills Bank at https://github.com/aliyun/qwen-dianjin.