C172 pilot reported runway excursion during landing roll out when they encountered a gust of wind. Pilot shut down engine and applied braking.

Narrative

While landing at ZZZ on Runway XXL the aircraft encountered significant crosswinds during my initial approach; prompting me to execute a go-around for another landing attempt.During my second approach to Runway XXL; I maintained a stable descent towards the runway. Employing a forward slip technique; I prepared for landing. Upon initiating the flare; the left main gear touched down first; followed by the right main gear. As I maintained back pressure on the elevator; the nose wheel made contact with the runway. After rolling approximately 1000 feet down the runway center past Taxiway 1; a gust of wind lifted the left wing; causing a sudden veer to the right towards the grassy area. In response; I swiftly pulled the mixture to cut off the engine and applied heavy braking. The right-wing tip briefly touched the grass as the momentum carried the aircraft into the grassy area; nearing Taxiway 2.Post-Incident: Conducted a thorough inspection of the aircraft for any damage resulting from the runway excursion. Reported the incident to air traffic control and relevant aviation authorities.Lessons Learned:Enhanced Awareness: Heightened awareness of gusty wind conditions and their potential impact on aircraft handling during the rollout.Improved Technique: I will review crosswind landing techniques to better manage challenging wind conditions with my flight instructor.