The ‘Bravo de Esmolfe’ apple (BE) is rich in antioxidants and represents one of the most important traditional cultivars in Portugal. A large amount of non-compliant BE, with no market value, it is generated every year. Thus, an effort to find value-added solutions is of utmost importance. For the first time, green extraction (microwave-assisted-extraction (MAE) and ultrasound-assisted-extraction (UAE)) were compared against conventional extraction (with (CET) and without temperature (CE)) to select the most efficient process to produce a natural antioxidant extract from non-compliant BE. The results showed that MAE and CET are good methodologies for developing a BE antioxidant extract. However, MAE is more sustainable than CET, requiring less time to reach high temperatures. The MAE-extract showed great antioxidant activity (14.80 ± 0.70 mg TE/g DE by ORAC, 3.92 ± 0.25 mg AAE/g DE by ABTS, and 5.11 ± 0.13 mg TE/g DE by DPPH). This extract revealed high amount of chlorogenic acid (0.48 ± 0.07 mg/g DE), (−)-epicatechin (0.30 ± 0.02 mg/g DE) and phloridzin (0.13 ± 0.01 mg/g DE). This study shows that non-compliant BE is a useful source of antioxidants, being a sustainable way for the recovery of value-added compounds from the rejected fruit in line with sustainable and circular bioeconomy principles.