Auto-ignition of turbulent non-premixed systems is encountered in practical devices such as diesel internal combustion engines. It remains a challenge for modellers, as it exhibits specific features such as unsteadiness, flame propagation and combustion far from stoichiometric conditions. In this paper, a two-dimensional DNS database of an igniting H-2/O-2/N-2 mixing layer, including detailed chemistry and transport, is extensively post-processed in order to gain physical insight into the flame structure and dynamics during auto-ignition. The results are used as a framework for the development of a generalized flame surface density modelling approach by integrating the equations over all possible mixture fraction values. The mean reaction rate is split into two contributions: a generalized flame surface density and a mean reaction rate per unit generalized flame surface density. The unsteadiness of the ignition phenomenon is accounted for via a generalized progress variable. Closures for the generalized surface average of the reaction rate and for the generalized progress variable are proposed, and the modelling approach is tested a priori versus the DNS data. The use of a laminar database for the chemistry coupled to the mean turbulent field via the generalized progress variable shows very promising results, capturing the correct ignition delay and the premixed peak in the turbulent mean heat release rate evolution. This allows confidence in future inclusion and validation of this approach in a RANS-CFD code.