  The observed correlation between outer giant planets and inner super-Earths
is emerging as an important constraint on planet formation theories. In this
study we focus on Kepler-167, which is currently the only system known to
contain both inner transiting super-Earths and a confirmed outer transiting gas
giant companion beyond 1 au. Using long term radial velocity monitoring, we
measure the mass of the gas giant Kepler-167e ($P=1071$ days) to be
$1.01^{+0.16}_{-0.15}$ M$_{\rm J}$, thus confirming it as a Jupiter analog. We
re-fit the $Kepler$ photometry to obtain updated radii for all four planets.
Using a planetary structure model, we estimate that Kepler-167e contains
$66\pm19$ M$_{\oplus}$ of solids and is significantly enriched in metals
relative to its solar-metallicity host star. We use these new constraints to
explore the broader question of how systems like Kepler-167 form in the pebble
accretion framework for giant planet core formation. We utilize simple disk
evolution models to demonstrate that more massive and metal-rich disks, which
are the most favorable sites for giant planet formation, can also deliver
enough solids to the inner disk to form systems of super-Earths. We use these
same models to constrain the nature of Kepler-167's protoplanetary disk, and
find that it likely contained $\gtrsim 300$ M$_{\oplus}$ of dust and was
$\gtrsim 40$ au in size. These values overlap with the upper end of the
observed dust mass and size distributions of Class 0 and I disks, and are also
consistent with the observed occurrence rate of Jupiter analogs around sun-like
stars.
