A broadband microwave photonic phase shifter based on a single III-V microdisk resonator heterogeneously integrated on and coupled to a nanophotonic silicon-on-insulator waveguide is reported. The phase shift tunability is accomplished by modifying the effective index through carrier injection. A comprehensive semi-analytical model aiming at predicting its behavior is formulated and confirmed by measurements. Quasi-linear and continuously tunable 2π phase shifts at radiofrequencies greater than 18 GHz are experimentally demonstrated. The phase shifter performance is also evaluated when used as a key element in tunable filtering schemes. Distortion-free and wideband filtering responses with a tuning range of ~100% over the free spectral range are obtained.