This paper investigates the dynamic relationship between the oil market and European stock market returns using monthly data from May 2007 to April 2022 for 27 European Union member countries. A novel approach is adopted by using the time-varying Granger causality test and the structural vector auto-regression model to examine the causal links. Empirical results reveal strong evidence of time-varying causation between the variables, considering the oil market from both the supply-side and demand-side perspectives. In light of these findings, numerous policy considerations emerge, including refining risk management strategies for investors, reformulating economic and energy policies, the potential impact on monetary policy decisions, the need for ad hoc market regulations, facilitating investor education initiatives, promoting international cooperation, and advancing the transition to sustainable energy sources.