Hesperidin and rutin are two sought-after natural flavonoids, traditionally extracted from abundant natural citrus fruits and tea leaves using large amounts of ethanol or methanol solvents. Recent trends in extractions have focused on minimizing the use of solvents and creating simpler cost-effective processes. This study aims to apply the concept of chemical valorization in the context of a circular economy, by using agro-industrial waste and biobased alternatives to traditional solvents, which are of environmental concern. We use minimum amounts of solvent/sample (5 mL/0.25 or 0.5 g) to extract hesperidin and rutin in a single-stage solid-liquid extraction. Thirty individual solvents and HSPiP were applied to find the best solvents/blends for extraction. The type of solvent, sample preparation, maceration time, and extraction temperature were studied. Results showed that the biobased solvent Cyrene is very effective when mildly heated to 65 °C (up to 91%) or mixed with water. Adding water to Cyrene forms its geminal diol hydrate, this enhances the solubility and extraction of hesperidin and rutin up to ten times than those of the original pure ketone form. Quantitative sustainability metrics from the CHEM21 Toolkit demonstrated that our extraction methodology is environmentally friendly and offers future potential of isolation of other flavonoids.