  The JWST discovery of ``little red dots'' (LRDs) is reshaping our picture of
the early Universe, yet the physical mechanisms driving their compact size and
UV-optical colors remain elusive. Here we report an unusually bright LRD
($z=3.1$) observed as part of the RUBIES program. This LRD exhibits broad
emission lines (FWHM $\sim4000$km/s), a blue UV continuum, a clear Balmer break
and a red continuum sampled out to rest 4 $\mu$m with MIRI. We develop a new
joint galaxy and AGN model within the Prospector Bayesian inference framework
and perform spectrophotometric modeling using NIRCam, MIRI, and NIRSpec/Prism
observations. Our fiducial model reveals a $M_*\sim 10^9M_\odot$ galaxy
alongside a dust-reddened AGN driving the optical emission. Explaining the
rest-frame optical color as a reddened AGN requires $A_{\rm v}\gtrsim4$,
suggesting that a great majority of the accretion disk energy is re-radiated as
dust emission. Yet despite clear AGN signatures, we find a surprising lack of
hot torus emission, which implies that either the dust emission in this object
must be cold, or the red continuum must instead be driven by a massive, evolved
stellar population of the host galaxy -- seemingly inconsistent with the high
EW broad lines (H$\alpha$ EW $\sim800$\AA). The widths and luminosities of
Pa$\beta$, Pa$\delta$, Pa$\gamma$, and H$\alpha$ imply a modest black hole mass
of $M_{\rm BH}\sim10^8M_\odot$. Additionally, we identify a narrow blue-shifted
HeI absorption in G395M spectra, signaling an ionized outflow with kinetic
energy up to $\sim1$\% the luminosity of the AGN. The low redshift of
RUBIES-BLAGN-1 combined with the depth and richness of the JWST imaging and
spectroscopic observations provide a unique opportunity to build a physical
model for these so-far mysterious LRDs, which may prove to be a crucial phase
in the early formation of massive galaxies and their supermassive black holes.
