We study the properties of two-photon cavity solitons that appear in a broad-area cascade laser. These vectorial solitons consist of islands of two-photon emission emerging over a background of single-photon emission. Analysis of their structural properties reveals singular features such as their short distance radiation of outgoing waves, which can be interpreted in terms of the soliton frequency profile. However, the phase of these solitons is not determined by any external factor, which influences the way in which the structures can be written and erased. We also examine ways of controlling the cavity–soliton position, and analyse the interaction between neighbouring cavity solitons. Finally, investigation of the parameter dependence of these structures shows a route from soliton-dominated to defect-mediated turbulence.