Apple by-products (i.e., peels) are often thrown away, yet they are highly nutritious and provide numerous advantages as they contain a variety of nutrients such as vitamins, minerals, and antioxidants. Apple peels also comprise a high level of antioxidants, particularly polyphenols and flavonoids. This research aimed to determine the most efficacious extraction techniques and parameters to accomplish maximum bioactive compounds recovery from apple peels. Several extractions were conducted, including stirring, ultrasonication, and pulsed electric field-assisted extractions. Response surface methodology and several factors such as temperature, extraction duration, and solvent composition were considered to have a major impact on the isolation of bioactive compounds. The findings indicated that the most practical and efficient approach was to combine the pulsed electric field process with ultrasonication and stirring at 80 °C for 30 min, while 75% aqueous ethanol comprised the optimal solvent concentration, demonstrating the critical role of the solvent in optimizing extraction efficiency. The optimal conditions were obtained through response surface methodology with a statistical significance of p < 0.05. The extract exhibited a total polyphenolic content (TPC) of 17.23 mg gallic acid equivalents (GAE) per g of dry weight (dw), an ascorbic acid content (AAC) of 3.99 mg/g dw, and antioxidant activity of 130.87 μmol ascorbic acid equivalents (AAE)/g dw, as determined by FRAP and 95.38 μmol AAE/g dw from the DPPH assay. The measured antioxidant activity highlighted the significant potential of apple peels as a cost-effective source of exceptionally potent extracts.