The inclusive electron neutrino charged-current cross section is measured in the NOvA near detector using 8.02×10^{20} protons-on-target in the NuMI beam. The sample of GeV electron neutrino interactions is the largest analyzed to date and is limited by ≃17% systematic rather than the ≃7.4% statistical uncertainties. The double-differential cross section in final-state electron energy and angle is presented for the first time, together with the single-differential dependence on Q^{2} (squared four-momentum transfer) and energy, in the range 1 GeV≤E_{ν}<6 GeV. Detailed comparisons are made to the predictions of the GENIE, GiBUU, NEUT, and NuWro neutrino event generators. The data do not strongly favor a model over the others consistently across all three cross sections measured, though some models have especially good or poor agreement in the single differential cross section vs Q^{2}.