  Using the entire BaBar $\Upsilon(4S)$ data set, the first two-dimensional
unbinned angular analysis of the semileptonic decay $\overline{B} \rightarrow D
\ell^- \overline{\nu}_\ell$ is performed, employing hadronic reconstruction of
the tag-side $B$ meson from $\Upsilon(4S)\to B\overline{B}$. Here, $\ell$
denotes the light charged leptons $e$ and $\mu$. A novel data-driven
signal-background separation procedure with minimal dependence on simulation is
developed. This procedure preserves all multi-dimensional correlations present
in the data. The expected $\sin^2\theta_\ell$ dependence of the differential
decay rate in the Standard Model is demonstrated, where $\theta_\ell$ is the
lepton helicity angle. Including input from the latest lattice QCD calculations
and previously available experimental data, the underlying form factors are
extracted using both model-independent (BGL) and dependent (CLN) methods.
Comparisons with lattice calculations show flavor SU(3) symmetry to be a good
approximation in the $B_{(s)}\to D_{(s)}$ sector. Using the BGL results, the
CKM matrix element $|V_{cb}|=(41.09\pm 1.16)\times 10^{-3}$ and the Standard
Model prediction of the lepton-flavor universality violation variable
$\mathcal{R}(D)=0.300\pm 0.004$, are extracted. The value of $|V_{cb}|$ from
$\overline{B} \rightarrow D \ell^- \overline{\nu}_\ell$ tends to be higher than
that extracted using $\overline{B} \rightarrow D \ell^- \overline{\nu}_\ell$.
The Standard Model $\mathcal{R}(D)$ calculation is at a $1.97\sigma$ tension
with the latest HFLAV experimental average.
