This paper introduces VESPA (Visual Event-Stream Progressive Analytics), a framework that integrates Streaming Process Mining (SPM) with Progressive Visual Analytics (PVA) to support timely, informed decisions using partial, evolving data. VESPA addresses the challenges of analyzing transient, multifaceted event-streams by coupling process mining with progressive visualizations. Our framework is structured around key dimensions (context, task, data, algorithm, user roles, and interaction modalities). Two central research questions guide our work: identifying optimal timing for progressive visualizations and determining their effectiveness and appropriateness in streaming contexts. A prototype with ward-centric and patient-centric views was conceptualized, based on a simulated real-world scenario in the context of an emergency department (ER). These views support user roles from passive monitoring to active exploration, enabling dynamic prioritization and resource allocation. Preliminary results demonstrate the potential of VESPA to enhance situational awareness and decision-making.