Summary: This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In contrast to the classical conservative four-equation model formulation, the adopted set of equations features volume fraction, temperature, velocity and pressure as the primary variables. The model includes the effects of viscosity, surface tension, thermal conductivity and gravity, and has the ability to incorporate complex equations of state. Additionally, a Gibbs free energy relaxation procedure is used to model mass transfer. A key characteristic of the proposed methodology is the use of high performance and scalable solvers for the solution of the Helmholtz equation for the pressure, which drastically reduces the computational cost compared to analogous density-based approaches. We demonstrate the capabilities of the methodology to simulate flows with large density and viscosity ratios through extended verification against a range of different test cases. Finally, the potential of the methodology to tackle challenging phase change flows is demonstrated with the simulation of three-dimensional nucleate boiling.