A strong optical nonlinearity arises when coherent light is scattered by a semiconductor quantum dot coupled to a nanophotonic waveguide. We exploit the Fano effect in such a waveguide to control the phase of the quantum interference underpinning the nonlinearity, experimentally demonstrating a tunable quantum optical filter which converts a coherent input state into either a bunched or an antibunched nonclassical output state. We show theoretically that the generation of nonclassical light is predicated on the formation of a two-photon bound state due to the interaction of the input coherent state with the quantum dot. Our model demonstrates that the tunable photon statistics arise from the dependence of the sign of two-photon interference (either constructive or destructive) on the detuning of the input relative to the Fano resonance.