Using the entire BABAR gamma(4S) dataset, the first two-dimensional unbinned angular analysis of the semileptonic decay (B) over bar -> Dl(-)(v) over bar (l) is performed, employing hadronic reconstruction of the tag-side B meson from gamma(4S) -> B (B) over bar. Here, l denotes the light charged leptons e and mu. Anovel data-driven signal-background separation procedure with minimal dependence on simulation is developed. This procedure preserves all multidimensional correlations present in the data. The expected sin(2) theta(l) dependence of the differential decay rate in the Standard Model is demonstrated, where theta(l) 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) -> D-(s) sector. Using the BGL results, the CKM matrix element vertical bar V-cb vertical bar = (41.09 +/- 1.16) x 10(-3) and the Standard Model prediction of the lepton-flavor universality violation variable R(D) = 0.300 +/- 0.004, are extracted. The value of vertical bar V-cb vertical bar from (B) over bar -> Dl(-)(v) over bar (l) tends to be higher than that extracted using (B) over bar -> Dl(-)(v) over bar (l). The Standard Model R(D) calculation is at a 1.97 sigma tension with the latest HFLAV experimental average.