A new computational methodology, termed "PeleLM-FDF" is developed and utilized for high fidelity large eddy simulation (LES) of complex turbulent combustion systems. This methodology is constructed via a hybrid scheme combining the Eulerian PeleLM base flow solver with the Lagrangian Monte Carlo simulator of the filtered density function (FDF) for the subgrid scale reactive scalars. The resulting methodology is capable of simulating some of the most intricate physics of complex turbulence-combustion interactions. This is demonstrated by LES of a non-premixed CO/H 2 temporally evolving jet flame. The chemistry is modelled via a skeletal kinetics model, and the results are appraised via detail a posteriori comparisons against direct numerical simulation (DNS) data of the same flame. Excellent agreements are observed for the time evolution of various statistics of the thermo-chemical quantities, including the manifolds of the multi-scalar mixing. The new methodology is capable of capturing the complex phenomena of flame-extinction and re-ignition at a 1/512 of the computational cost of the DNS. The high fidelity and the computational affordability of the new PeleLM-FDF solver warrants its consideration for LES of practical turbulent combustion systems.