Integrated microspectrometers implemented in silicon photonic chips have gathered a great interest for diverse applications such as biological analysis, environmental monitoring, and remote sensing. These applications often demand high spectral resolution, broad operational bandwidth, and large optical throughput. Spatial heterodyne Fourier-transform (SHFT) spectrometers have been proposed to overcome the limited optical throughput of dispersive and speckle-based on-chip spectrometers. However, state-of-the-art SHFT spectrometers in near-infrared achieve large optical throughput only within a narrow operational bandwidth. Here we demonstrate for the first time, to the best of our knowledge, a broadband silicon nitride SHFT spectrometer with the largest light collecting multiaperture input (320×410µm2) ever implemented in an SHFT on-chip spectrometer. The device was fabricated using 248 nm deep-ultraviolet lithography, exhibiting over 13 dB of optical throughput improvement compared to a single-aperture device. The measured resolution varies between 29 and 49 pm within the 1260-1600 nm wavelength range.