This paper proposes a non-linear New Keynesian Phillips curve J (Inv-L NK Phillips Curve) to explain the surge of inflation in the 2020s. Economic slack is measured as firms’ job vacancies over the number of unemployed workers. After showing empirical evidence of statistically significant non-linearities, we propose a New Keynesian model with search and matching frictions, complemented by a form of wage rigidity, in the spirit of Phillips (1958), that generates strong nonlinearities. Policy implications include the thesis that appropriate monetary policy can bring inflation down without a significant recession and that the recent inflationary surge was mostly generated by a “ labor short-age” – i.e. an exceptionally tight labor market, which in addition to triggering inflation pressures by itself, amplifies the impact of other supply shortages.