The key factors contributing to the formation and maintenance of the recently discovered extra-tropical tropopause inversion layer are presently unclear. In this study, it is shown that such a layer can form as a consequence of the turbulent dynamics of synoptic-scale baroclinic eddies alone, in the absence of explicitly parameterized, small-scale, radiative-convective processes. A simple general circulation model, initialized from a state of rest, and driven with idealized forcings, is found to spontaneously develop an inversion layer above the tropopause under a wide variety of parameter choices and model resolutions. Furthermore, such a model is able to capture, qualitatively, both the latitudinal and (in part) the seasonal dependence of the observed tropopause inversion layer. However, the inability of our simple model to capture some detailed quantitative features strongly suggests that other physical processes, beyond balanced synoptic-scale dynamics, are likely to play an important role.