Control of the combustion process in Spark-Ignition (SI) engines operated with extreme dilution from exhaust gas re-circulation (EGR) represents one of the major limitations in the industrial design of such technology. Numerical approaches able to describe in detail the formation of the early flame kernel become essential to face such an ambitious task. This work presents a RANS-based multi-dimensional model of the combustion process, including an advanced description of the ignition stage to consider its stochastic re-ignitions within the average cycle prediction. The spark-channel is described as a column of Lagrangian parcels that represent early flame kernels, whose growth is controlled by the laminar flame speed and energy input from the electrical circuit. The spatial evolution of each parcel is computed according to a scaled value of the average-flow speed, to mimic the smooth but short elongation of the mean-cycle channel produced by stochastic restrikes affecting the single-cycle arcs. To clarify this phenomenon and assess the proposed CFD method, a series of experiments are performed in a single cylinder SI engine with optical access, running at a low-load cruise-speed operating condition. Increasing EGR levels are tested up to the onset of misfire, with measurements of the secondary-circuit features and of the flame evolution through high-speed imaging. Satisfactory results are achieved in terms of numerical-experimental comparison of the cycle-averaged in-cylinder pressure, discharge parameters, and spatial flame distribution, demonstrating the reliability of the proposed numerical approach.