Studies of dark matter lie at the interface of collider physics, astrophysics and cosmology, and they entail comparisons with a wide spectrum of data. We consider an effective top-philic t-channel model of dark matter, which finds some motivation in composite theories. We make use of a general framework allowing for precision predictions from the sole knowledge of the model’s Lagrangian to investigate the resulting phenomenology both at colliders and in cosmology. We then explore some of the non-minimal features of the model, and we additionally highlight overlooked search channels that are relevant for generalised version of the models.