The Neutron Star Interior Composition Explorer (NICER) has extensively monitored the 2019 August outburst of the 401 Hz millisecond X-ray pulsar SAX J1808.4–3658. In this Letter, we report on the detection of a bright helium-fueled Type I X-ray burst. With a bolometric peak flux of (2.3 ± 0.1) × 10−7 erg s−1 cm−2, this was the brightest X-ray burst among all bursting sources observed with NICER to date. The burst shows a remarkable two-stage evolution in flux, emission lines at 1.0 and 6.7 keV, and burst oscillations at the known pulsar spin frequency, with ≈4% fractional sinusoidal amplitude. We interpret the burst flux evolution as the detection of the local Eddington limits associated with the hydrogen and helium layers of the neutron star envelope. The emission lines are likely associated with Fe, due to reprocessing of the burst emission in the accretion disk.