A 2DH highly nonlinear Boussinesq-type of model for breaking waves has been developed in order to investigate surf zone hydrodynamics, also in the presence of complex bathymetries. The set of equations includes continuity and rotational momentum equations, coupled with the vorticity transport equation. An appropriate spatial definition of the 3D roller concept, along with an algorithm for accurately tracking the roller position, have been on purposely developed. Several numerical simulations have been carried out for the case of a submerged elliptic shoal. The results have been compared with both experimental data and with the results of other numerical models available in the literature. Finally, the vorticity dynamics under a breaking wave has been analyzed both in time and space, showing that a fairly correct interpretation of the wake effect in the rear part of the wave crest is obtained.