In this paper a planar electromagnetic absorber is introduced whose performance is maintained over a wide change of the incidence angle for both TE and TM polarization. The absorber comprises an array of patches over a grounded dielectric slab, with clear advantage in terms of manufacturability. It is shown that a high value of the relative permittivity of the substrate is essential for the operation of the absorber. The main contribution of the paper is to demonstrate and practically use the presence of an additional resonance of high-impedance surfaces when the plasma frequency of the wire medium comprising metallic vias in the dielectric substrate is close to the original resonance of the high-impedance surface. The presence of the vias between FSS and the ground plane is discussed both for the case of a high-permittivity absorber and for a low permittivity one. The radius of the vias influences the oblique incidence TM absorption, and when properly designed, the insertion of the vias result in bandwidth enlargement and higher absorption.