This study examines a low-processed, food-grade extraction concept for peppermint leaves (Mentha × piperita L.) using solvents consistent with the principles of green chemistry and an infusion-like protocol. Primary extraction (2–30 min; 50–100 °C) was carried out using water, plasma-treated nanowater, a glycerol–water mixture (65%), an ethanol–water mixture (50%; at room temperature and at 50 °C), and rapeseed oil. To evaluate the potential use of biomass within a circular economy model, the residue remaining after the first extraction was subjected to secondary extraction under identical time–temperature conditions. Primary and secondary extracts were characterized in terms of total phenolic content (TPC), total flavonoid content (TFC), essential oil (EO) recovery, and antioxidant activity (DPPH and FRAP), and extraction yields were expressed relative to a 70% methanolic reference (TPC/TFC) and to the initial EO content in the plant material. Under the most favorable conditions (10 min; 100 °C; ethanol–water at 50 °C), the highest extraction yields of polar phytochemicals (TPC and TFC) were obtained with water and nanowater, whereas the ethanol–water mixture (50%) and rapeseed oil provided the greatest recovery of essential oil (up to complete depletion after the second extraction). Antioxidant activity showed a similar dependence on solvent type, with water and nanowater extracts exhibiting the highest DPPH/FRAP values. Importantly, secondary extraction contributed a substantial share of the total recovered bioactive compounds (often >30% of combined TPC/TFC), confirming that post-extraction residues remain a valuable raw material. The results support a practical, sequential strategy for designing peppermint extracts: aqueous and glycerol systems for phenolic-rich extracts, and ethanol and oil systems for essential-oil-enriched preparations, with secondary extraction enabling simple, low-energy biomass valorization.