This paper presents a fundamental study of ultra-lean flames stabilized behind a thin, highly conducting metallic rectangular bluff body acting as a flame holder. Using high fidelity numerical simulations, we reproduce a phenomenon observed experimentally, showing that in this configuration steady hydrogen–methane flames can exist at equivalence ratios below the flammability limit associated with planar unstrained flames with the same hydrogen–methane proportion. These ultra–lean hydrogen–enriched mixtures exhibit a distinct stabilization mechanism compared to pure methane flames: they stabilize in the form of inverted closed V or U flames farther away from the flame holder as the inflow reactants velocity is reduced, leading eventually to blow-off for sufficiently small velocities. Conversely, as the reactants flow rate is increased, the flames anchor closer to the flame holder, and surprisingly no blow-off is observed at high velocities. This response is shown to be linked to the presence of hydrogen in the fuel mixture and its large diffusivity, which results in locally richer mixtures in the strained, curved flame base.