The development of a small-scale, secondary roll-up in an incompressible, inviscid, variable-density, high Froude number, two-dimensional mixing layer is numerically investigated using the Transport Element Method. The numerical scheme consists in following a collection of elements carrying the local value of both the vorticity field and the density gradient. High resolution simulations of the temporal and spatial models of the shear layer are performed. They allow to capture the small-scale structures appearing over the primary Kelvin-Helmholtz instability where the baroclinic torque intensifies the vorticity field. Those results in contrast with the uniform density case, reveal the features of the variable-density transition to turbulence in variable-density shear flows.