Despite all their advantages, load-bearing concrete shell structures with double curvatures are not frequently in use. The main reason is the complexity of their construction. In such a context, this article starts with a brief, critical review of existing technologies while their pros and cons are highlighted. Against that background, the authors propose a new approach for the highly automated fabrication of gridshell structures from variable modules reinforced with textile meshes. To demonstrate the feasibility of such a new technology, a demonstrator called ConDIT 1.0, a sphere-like shell structure composed of several frames, was designed and built. The frame modules were fabricated automatically using extrusion-based 3D printing and a printable, strain-hardening cement-based composite (SHCC). This article presents the design of ConDIT 1.0, the mechanical material characterization of printed SHCC, the technology of module production, the results of geometry verification for print modules using 3D scanning, and the procedure for the demonstrator’s assembly.