High-resolution broadband spectroscopy at near-infrared wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar. Observations of stars were performed with the “TEDI” interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec near-infrared echelle spectrograph. These are the first multidelay EDI demonstrations on starlight, as earlier measurements used a single delay or laboratory sources. We demonstrate very high () resolution boost, from original 2700 to 27,000 with current set of delays (up to 3 cm), well beyond the classical limits enforced by the slit width and detector pixel Nyquist limit. Significantly, the EDI used with multiple delays rather than a single delay as used previously yields an order of magnitude or more improvement in the stability against native spectrograph point spread function (PSF) drifts along the dispersion direction. We observe a dramatic () reduction in sensitivity to PSF shift using our standard processing. A recently realized method of further reducing the PSF shift sensitivity to zero is described theoretically and demonstrated in a simple simulation which produces a times reduction. We demonstrate superb rejection of fixed pattern noise due to bad detector pixels—EDI only responds to changes in pixel intensity synchronous to applied dithering. This part 1 describes data analysis, results, and instrument noise. A section on theoretical photon limited sensitivity is in a companion paper, part 2.