We present high-resolution (R similar or equal to 18,000), high signal-to-noise 2 mum spectra of two luminous, X-ray flaring Class I protostars in the rho Ophiuchi cloud acquired with the NIRSPEC spectrograph of the Keck II telescope. We present the first spectrum of a highly veiled, strongly accreting protostar, which shows photospheric absorption features and demonstrates the stellar nature of its central core. We find the spectrum of the luminous (L-bol = 10 L.) protostellar source, YLW 15, to be stellar-like with numerous atomic and molecular absorption features, indicative of a K5 IV/V spectral type and a continuum veiling r(k) = 3.0. Its derived stellar luminosity (3 L.) and stellar radius (3.1 R.) are consistent with those of a 0.5 M. pre-main-sequence star. However, 70% of its bolometric luminosity is due to mass accretion, whose rate we estimate to be 1.6 x 10(6) M. yr(-1), onto the protostellar core. We determine that excess infrared emission produced by the circumstellar accretion disk, the inner infalling envelope, and accretion shocks at the surface of the stellar core of YLW 15 all contribute significantly to its near-IR continuum veiling. Its projected rotation velocity v sin i = 50 km s(-1) is comparable to those of at-spectrum protostars, but considerably higher than those of classical T Tauri stars in the rho Oph cloud. The protostar may be magnetically coupled to its circumstellar disk at a radius of 2 R-*. It is also plausible that this protostar can shed over half its angular momentum and evolve into a more slowly rotating classical T Tauri star by remaining coupled to its circumstellar disk (at increasing radius) as its accretion rate drops by an order of magnitude during the rapid transition between the Class I and Class II phases of evolution. The spectrum of WL6 does not show any photospheric absorption features, and we estimate that its continuum veiling is r(k)greater than or equal to4.6. Its low bolometric luminosity (2 L.) and high veiling dictate that its central protostar is very low mass, M similar to 0.1 M..