Achieving strong light-matter interactions at the single photon level is an important milestone of the quantum technologies roadmap. Recently, the quantum optics and quantum information communities have witnessed the emergence of waveguide quantum electrodynamics (waveguide QED), where the atom-photon interaction is increased without cavity by using subwavelength waveguides that confine the electromagnetic field to deeply subwavelengths scales in the transverse directions. Different waveguide QED platforms coexist, each one having its own advantages and drawbacks: superconducting qubits coupled to transmission lines at microwave frequencies, quantum dots in nanophotonic structures, and cold atoms trapped along a nanofiber. However, currently, no system can provide both many emitters and a high coupling strength. This interaction regime is largely unexplored in waveguide QED. The eQUANDIS project has the ambition to realize for the first time non-linear quantum optics experiments in this regime. We target the realization of a single-photon switch. Moreover, because of the lack of atom-compatible structures with an engineered dispersion, the impact of the waveguide dispersion has been scarcely investigated in waveguide QED studies. Its role in the formation of the collective properties of an atomic ensemble is still unknown. The eQUANDIS project aims at filling this blank page by implementing a waveguide QED platform based on cold atoms trapped along slow-light waveguides whose dispersion can be engineered through symmetry breaking. The transverse symmetry breaking in this type of photonic-crystal waveguides allows us to engineer the dispersion beyond the usual parabolic shape. The eQUANDIS project brings together 5 teams with complementary competences: theoretical and computational nanophotonics, inverse design with advanced optimization algorithms, nanofabrication, quantum-optics theory, quantum-optics experiments with ensembles of cold atoms.