This work presents a new computational framework for designing profile extrusion dies. The framework utilizes High-Performance Computing (HPC) resources to optimize parameterized die flow channels within a one-day time-frame, resulting in a significant reduction in the typical design time required for profile extrusion dies. By employing objective function-controlled convergence criteria, the framework achieved a 50% reduction in calculation time compared to runs where only the unknowns residuals were considered for the same purpose. Furthermore, it offers full optimization capability, requiring no user intervention once the CAD parameterization is complete. OpenFOAM and Dakota were employed for modeling and optimization, respectively. Fusion 360 and Onshape CAD software were used for drawing and parameterizing the flow channel. By leveraging HPC systems, the optimization framework can automatically test hundreds of alternative geometries within one day to find the optimal solution. This research demonstrates the feasibility and advantages of HPC-driven extrusion die optimization, which contributes to increased efficiency and competitiveness in the manufacturing industry.