The aim of this article is to propose a new general methodology to measure job polarization and empirically analyses the degree of polarization from the demand side of the European Union market at regional level during the post COVID-19 period. Unlike most studies that examine polarization from the supply side, typically measured by shifts in employment shares across the occupational skill spectrum, focusing on the simultaneous growth of high-skill and low-skill jobs, this research approaches polarization from the unmet demand side. Methodologically, we applied Self-Organizing Maps for clustering and Generalized Joint Regression models, which offered considerable flexibility in modeling labor market polarization, while also addressing issues of sample selection and covariate endogeneity. This methodological framework naturally provides a new model-based index of polarization. Empirically, we analyzed institutional EU data from Cedefop, which includes job advertisements posted on online portals across the EU, categorized by region and main (ESCO) occupational groups. Conducting this analysis at the regional level in the post-pandemic period addresses significant gaps in the literature. Empirical findings highlight several pressing issues in the European labor market post-pandemic, including strong labour demand polarization, high-skill occupation saturation and educational mismatches (overqualification), particularly affecting women. To our knowledge, this is the first study to focus on job polarization from the demand side, employing flexible models to jointly model polarization and the demand for specific occupations in term of main determinants at the regional level, while integrating regional data from the Labour Force Survey and online job advertisements from Cedefop data.