Here, we show that the electronic properties of a surface-supported 2-dimensional (2D) layer structure can self-texturize at nanoscale. The local electronic properties are determined by structural relaxation processes through variable adsorption stacking configurations. We demonstrate that the spatially modulated layer-buckling, which arises from the lattice mismatch and the layer/substrate coupling at the GdAu2/Au(111) interface, is sufficient to locally open an energy gap of ∼0.5 eV at the Fermi level in an otherwise metallic layer. Additionally, this out-of-plane displacement of the Gd atoms patterns the character of the hybridized Gd-d states and shifts the center of mass of the Gd 4f multiplet proportionally to the lattice distortion. These findings demonstrate the close correlation between the electronic properties of the 2D-layer and its planarity. We demonstrate that the resulting template shows different chemical reactivities which may find important applications.