Large Eddy Simulations of the Sydney mixed-mode flame with inhomogeneous inlet (FJ200-5GP-Lr75-57) are performed using the Eulerian Stochastic Fields (ESF) transported probability functions method to account for the sub-grid scale turbulence–chemistry interaction, to demonstrate the suitability of the ESF method for mixed-mode combustion. An analytically reduced 19-species methane mechanism is used for the description of the chemical reactions. Prior to the reactive case, simulation results of the non-reactive setup with cold and hot pilot stream are presented, which show differences in the jet breakup and radial species mass fluxes. The reactive case simulations are compared to experimental data and a recently conducted model free quasi-DNS (qDNS), showing very good agreement with the qDNS in terms of scatter data and radial mean values of temperature and species distribution, as well as mixture fraction conditional statistics. Further analysis is dedicated to sub-grid scale statistics, showing that mixture fraction and reaction progress variable are strongly correlated in this flame. The impact of the number of stochastic fields on the filtered temperature and species distribution is investigated; it reveals that the ESF method in conjunction with finite-rate chemistry is very insensitive to the number of employed fields to obtain highly accurate simulation results.