One illustrative IC product disclosed herein includes first and second final gate structures and an insulating gate separation structure positioned between the first and second final gate structures. In one embodiment, the insulating gate separation structure has a stepped bottom surface with a substantially horizontally oriented bottom central surface that is surrounded by a substantially horizontally oriented recessed surface, wherein the substantially horizontally oriented bottom central surface is positioned a first level above the substrate and the substantially horizontally oriented recessed surface is positioned at a second level above the substrate, wherein the second level is greater than the first level.