We present a novel laser-based ion acceleration scheme, where a petawatt circularly polarized laser pulse is shot on an ultra-thin (nano-scale) double-layer target. Our scheme allows the production of high-quality light ion beams with both energy and angular dispersion controllable by the target properties. We show that extraction of all electrons from the target by radiation pressure can lead to a very effective two-step acceleration process for light ions if the target is correctly designed. Relativistic protons are predicted with pulse powers of a few petawatts. Careful analytical modeling yields estimates for characteristic beam parameters and requirements on the laser pulse quality, in excellent agreement with one- and two-dimensional particle-in-cell simulations.