This study focuses on optimizing double stir casting process parameters to enhance the tensile strength of hybrid composites comprising aluminum alloy, brown pumice, and coal ash, intended for brake disc applications. Analytical techniques including X-ray fluorescence, X-ray diffraction, thermogravimetric analysis, and scanning electron microscopy were employed to characterize the composite constituents. The Taguchi method was utilized for experimental design and optimization to determine the optimal weight compositions of brown pumice and coal ash, as well as stir casting parameters (stirrer speed, pouring temperature, and stirring duration). Regression analysis was employed to develop a predictive mathematical model for the tensile strength of the hybrid composites and to assess the significance of process parameters. The optimized composite achieved a predicted tensile strength of 186.81 MPa and an experimental strength of 190.67 MPa using 7.5 vol% brown pumice, 2.5 vol% coal ash, a pouring temperature of 700 °C, stirrer speed of 500 rpm, and stirring duration of 10 min. This represents a 52.23% improvement over the as-cast aluminum alloy’s tensile strength. Characterization results revealed that brown pumice and coal ash contain robust minerals (SiO2, Fe2O3, Al2O3) suitable for reinforcing metal matrices like aluminum, titanium, and magnesium. Thermogravimetric and differential thermal analyses demonstrated thermal stability up to 614.01 °C for the optimized composite, making it suitable for brake disc applications.