Air carrier pilot on approach reported abnormal engine readings and performance led them to shut down the engine and continue to land after troubleshooting.

Narrative

While on arrival into ZZZ operating Flight ABCD on Aircraft X; on the base leg for Runway XXL at approximately 3;000 feet MSL; the aircraft experienced a sudden jolt followed by noticeable airframe vibration as the the power was coming out from idle. Almost simultaneously; a burning odor was detected through the cockpit air vents.I immediately reviewed the upper ECAM and observed engine #2 exhibiting surging indications on the EPR (Engine Pressure Ratio) gauge and the noise made by the engine and with a rapidly increasing EGT. There were no associated ECAM and no fire warnings. I reduced thrust to that engine to idle power and went MCT (Maximum Continuous Thrust) on the good engine. We advised ATC and broke off the approach and took vectors so we could finish the checklist. Based on the abnormal engine parameters; surging condition; extremely high EGT and presence of a burning odor; I elected to shut down engine #2 by accomplishing the applicable QRH procedures for EGT Overlimits. Aircraft weight was verified to be below maximum landing weight.Dispatch was notified via ACARS; and the flight attendants were advised and issued a briefing. A single-engine approach and landing were conducted without further incident. After landing; the aircraft was stopped on the runway to allow fire rescue personnel to inspect engine #2. No evidence of external fire was observed. We then proceeded to taxied to the gate normally. A detailed logbook entry was made to document the event for maintenance troubleshooting.