Grape pomace represents 60%, by weight, of the solid side-streams of the wine-making process. The quantities produced, seasonality, and the presence of polyphenols pose economic and environmental issues that require proper management approaches based on the principles of sustainability and circular economy. The present work focuses on the combined application of solid–liquid extraction of polyphenols from ground grape pomace using a hydroethanolic mixture and the composting of the exhausted pomace. The obtained results support the possibility of recovering approximately 76.5 g of extract per kg of dry grape pomace (or 1.8 g of total phenols per kg of dry grape pomace). The composting process was not affected by the extraction process. On the contrary, the composting process was enhanced by the pomace particle size reduction, in terms of final biostability and content of humic acids.