Increasing research is being directed toward the production of value-added products using plant extracts that are super-fortified with antioxidants. In this study, the extraction parameters for bioactive compounds (such as polyphenols) from Nasturtium officinale leaves and their antioxidant properties were optimized using response surface methodology. The optimization procedure examined the effects of the extraction temperature, time, and solvent composition on conventional magnetic stirring (ST). In addition, the impacts of two green techniques—pulsed electric field (PEF) and ultrasound (US)—were evaluated individually and in combination to assess their potential to enhance the extraction of the compounds. According to our findings, under the proposed extraction conditions (a combination of PEF, US, and ST as a extraction technique, 50% ethanolic solvent, for 30 min at 80 °C). N. officinale leaf extract proved to be an excellent source of bioactive compounds, with extracts containing rosmarinic acid (3.42 mg/g dried weight (dw)), chlorogenic acid (3.13 mg/g dw), total polyphenol content (28.82 mg of gallic acid equivalents (GAE)/g dw), and strong antioxidant properties. The FRAP method measured 57.15 μmol ascorbic acid equivalents (AAE)/g dw, while the DPPH radical scavenging activity method measured 47.55 μmol AAE/g dw. This study was carried out to evaluate and improve the concentration of bioactive compounds in N. officinale leaf extract, resulting in a product with multiple applications across the food, cosmetic, and pharmaceutical industries.