We consider the inverse electromagnetic scattering problem of retrieving the shape of an inaccessible, perfectly electric conducting target from a set of far field measurements and develop a new reconstruction method in which the unknown scatterer is modeled by means of a surface impedance. The basic idea is to approximate the unknown object through a circular impedance cylinder enclosed in it and equipped with a suitable inhomogeneous surface impedance. By doing so, the ill-posedness and the nonlinearity of the underlying problem are then handled separately, through two successive processing steps. In the first step, the inhomogeneous surface impedance of the auxiliary scatterer is reconstructed through the regularized analytical continuation of the measured far-field data. Then, the unknown shape is retrieved through the solution of a nonlinear optimization problem aimed at determining the spatial locations where the field outside of the impedance target vanishes, in agreement with the boundary condition arising onto the unknown target. As demonstrated with several numerical results, the method is robust against uncertainties on data and provides quite accurate results for targets with starlike boundaries having both convex and concave parts.