Fast and precise spectrometers have numerous applications in quantum sciences, astronomy, and other fields. Thanks to the recent advances in the technology of single-photon detectors, their timing and spectral resolution approach fundamental limits dictated by the Heisenberg uncertainty principle (HUP) allowing new measurements, which were not possible before. In this work, we present a simple and fast spectrometer based on the LinoSPAD2 detector. With an array of 512 SPADs with a pixel size of 26 um2, we can achieve 0.1 nm/pixel spectral resolution with off-the-shelf optical components. Thanks to the 40 ps rms timing resolution of each SPAD, we can operate a factor of 10 above the HUP. We present measurements of the Hanbury Brown-Twiss effect at multiple frequencies using both the discrete spectral lines of a noble gas source and a broadband source of light (LED).