To achieve progress, we need to start thinking differently. This is the key aspect of additive manufacturing (AM) and 3D printing, which can trigger new, unconventional and high-performance designs in any engineering sector. This makes it possible to realize almost any geometry, paving the way to realize topology optimization (TO)-based designs, controlling the material distribution itself, thereby leaving ample room for imagination and optimization. The coupling of TO and AM is a powerful design tool, especially for building envelope components. The latter is the focus of our study as the building sector is among those industries requiring new perspectives and innovations to pursue energy transition and sustainable development. In this frame, AM is expected to be an effective tool to revolutionize the construction industry. AM 3D printed walls (3DPW) have proved to be sustainable, less expensive, and adaptable to various needs. However, without controlling the infill and shape of a 3DPW, its full potential cannot be exploited. This issue might be tackled resorting to TO for the fabrication of innovative engineered building wall elements characterized by reduction of raw material consumption while maximizing thermal resistance. Specifically, the optimization is performed under a fixed available volume and applying material distribution constraints, i.e., robust formulation and overhang constraint, in order to control the wall weight. Thus, the goal is to minimize the thermal conductance, i.e., to maximize the thermal resistance, by constraining the weight of the wall. 2D finite element simulations are carried out on different configurations under the winter design conditions of Naples, South Italy. Optimized designs are compared in terms of thermal conductance and velocity field inside the air cavities, to prove how topology optimization leads to limited air recirculation and thus higher thermal insulation.