We demonstrate a time-resolved terahertz (THz) system taking advantage of noncollinear frequency mixing in thick generation and detection crystals to perform broadband and high-sensitivity spectroscopy. A phase grating etched at the surface of a 2 mm-thick GaP crystal is used to control phase-matching conditions by diffracting near-infrared pulses. Our dual grating configuration allows long nonlinear interaction lengths that maximize THz generation and detection efficiencies while maintaining an accessible spectral window of 7 THz.