A turbulent mixing layer formed from two supersonic streams initially separated by a splitter plate is investigated with a hybrid computational method using Reynolds-averaged Navier-Stokes (RANS) approach for wall-bounded regions and a large-eddy simulation (LES) approach for the turbulent mixing region. Simulations of the mixing layer predict a vortex shedding originating from the splitter base and then a rapid transition to turbulence, which is in agreement with experimental observations. As a result, the potential of the hybrid method is demonstrated for flows in which a geometric feature, such as the blunt splitter plate considered here, provides the dominant unsteady feature leading to turbulence, without imposing additional inflow disturbances. Parametric studies of LES subgrid modeling settings, variations in the spanwise computational domain, and wall temperature settings in the RANS region were conducted. The subgrid model cases, using a baseline computational grid with small spanwise computational domain, overpredicted the mixing layer turbulence levels but only showed small variation in the mixing layer predictions with large changes in the model parameters. The cases examining wider spanwise domains enabled more turbulent energy to be released in the spanwise direction, which in turn reduced axial and vertical turbulence levels. Finally, prescribing the wall temperatures in the RANS regions instead of using the more traditional adiabatic wall boundary conditions further reduced turbulence levels and enabled reasonable agreement with experimental data.