The growing adoption of electric vehicles is expected to result in a significant increase in the volume of spent lithium-ion batteries (LIBs), highlighting the need for efficient and environmentally sustainable recycling methods. This study presents an optimized process for recovering critical metals—cobalt, nickel, manganese, and lithium—from spent LIBs. The method involves roasting followed by leaching using a deep eutectic solvent (DES) composed of propionic acid (PA), choline chloride (ChCl), and nitrilotriacetic acid (NTA), a chelating agent. Key operational parameters—including roasting temperature and duration, ChCl–PA molar ratio, leaching temperature and time, solid-to-liquid ratio, and NTA concentration—were systematically investigated. Roasting at 200 °C for 2 h improved leaching efficiencies of nickel and cobalt by 20.2% and 6.3%, respectively. Optimal leaching conditions were identified as 80 °C for 120 min with a solid-to-liquid ratio of 15 g/L. The addition of 0.07 M NTA shortened the leaching time from 120 to 60 min while achieving leaching efficiencies of 98.5% for lithium and 100% for cobalt, nickel, and manganese. Manganese was selectively separated from the leachate using D2EHPA, while cobalt, nickel, and lithium were subsequently recovered from the manganese-free solution using Cyphos IL 104 and oxalic acid. Leaching efficiency declined by 10–15% with each reuse of the DES. Overall, this approach offers a highly efficient and economically feasible strategy for metal recovery from spent LIBs, contributing to circular economy practices and sustainable battery waste management.