The solid oxide fuel cell can comprise: an electroconductive and porous reformer including a catalytically active material and shaped to constitute a solid slab having a first surface and a second surface opposite the first surface, and a plurality of adjacent grooves along the first surface, and flat regions adjacent the plurality of grooves; an anode layer covering the plurality of grooves of the reformer slab and having a corresponding grooved shape; an electrolyte layer covering the anode layer over the plurality of grooves of the reformer slab and having a corresponding grooved shape, and extending over the flat regions; and a cathode layer covering the electrolyte layer over the grooves of the reformer slab and having a corresponding grooved shape.