This comprehensive study delves into the Harmonised Consumer Price Index (HCPI) behavior across European economies from the early 2000s to the post-pandemic period. By analyzing the patterns of convergence and divergence in HCPI persistence, the study aims to uncover the common external and country-specific factors driving these dynamics. Utilizing the local Whittle estimation method, the research examines the longmemory properties of headline inflation through monthly data from January 1996 to January 2023. The study expands upon existing knowledge of inflation persistence by exploring its changes and the various patterns of inflation persistence in Europe. The findings reveal significant differences in the persistence of inflation and the underlying factors behind it. As such, the study emphasizes the need for tailored policy approaches and a deeper understanding of inflation's true nature, expectation formation, price-setting behavior, and monetary policy in shaping inflation persistence. Given its important policy implications, this research is highly relevant to the European Central Bank (ECB) and national governments within the Eurozone.