This paper describes the operation of a new design of wave energy converter. The design consists of a buoyant tethered submerged circular cylinder which is allowed to pitch freely about an axis below its centre. Within the body of the cylinder a fluid half fills an annular tank whose shaped inner walls allow the fundamental sloshing mode of the fluid be to tuned to any period of interest. The pitching motion of the cylinder in waves induces a sloshing motion inside the annular tank which in turns drives an air turbine connecting air chambers above the two isolated internal free surfaces. The concept behind this design is to couple resonances of the pitching cylinder with natural sloshing resonances of the internal water tank and thus achieve a broadbanded power response over a wide range of physically-relevant wave periods. Mathematically, the problem introduces new techniques to solve the series of complex internal forced sloshing problems that arise and to efficiently determine key hydrodynamic coefficients needed for the calculation of the power from the device. The results show that practical configurations can be found in which the efficiency of a two-dimensional cylindrical device is close to its maximum theoretical limit over the target range of periods from to s.