This research analyses the existence of structural breaks and the composition of convergence clubs in the EU-27 using GDP per capita (PPS) over 2003–2023. To this end, the Phillips–Sul log-t approach is combined with the Bai–Perron multiple structural break test. To the best of our knowledge, this is the first EU-27 convergence club analysis at the NUTS-3 level. The results suggest that incorporating structural breaks and highly disaggregated regional data improves the understanding of European convergence dynamics and may help reduce the risk of “accidental winners” in the allocation of EU cohesion funds.