High-multiplex and deep spectroscopic follow-up of upcoming panoramic deep-imaging surveys like LSST, Euclid, and WFIRST is a widely recognized and increasingly urgent necessity. No current or planned facility at a U.S. observatory meets the sensitivity, multiplex, and rapid-response time needed to exploit these future datasets. FOBOS, the Fiber-Optic Broadband Optical Spectrograph, is a near-term fiber-based facility that addresses these spectroscopic needs by optimizing depth over area and exploiting the aperture advantage of the existing 10m Keck II Telescope. The result is an instrument with a uniquely blue-sensitive wavelength range (0.31-1.0 um) at R~3500, high-multiplex (1800 fibers), and a factor 1.7 greater survey speed and order-of-magnitude greater sampling density than Subarus Prime Focus Spectrograph (PFS). In the era of panoramic deep imaging, FOBOS will excel at building the deep, spectroscopic reference data sets needed to interpret vast imaging data. At the same time, its flexible focal plane, including a mode with 25 deployable integral-field units (IFUs) across a 20 arcmin diameter field, enables an expansive range of scientific investigations. Its key programmatic areas include (1) nested stellar-parameter training sets that enable studies of the Milky Way and M31 halo sub-structure, as well as local group dwarf galaxies, (2) a comprehensive picture of galaxy formation thanks to detailed mapping of the baryonic environment at z~2 and statistical linking of evolving populations to the present day, and (3) dramatic enhancements in cosmological constraints via precise photometric redshifts and determined redshift distributions. In combination with Keck I instrumentation, FOBOS also provides instant access to medium-resolution spectroscopy for transient sources with full coverage from the UV to the K-band.