We report the first measurement of flux-integrated double-differential quasielastic-like neutrino-argon cross sections, which have been made using the Booster Neutrino Beam and the MicroBooNE detector at Fermi National Accelerator Laboratory. The data are presented as a function of kinematic imbalance variables which are sensitive to nuclear ground state distributions and hadronic reinteraction processes. We find that the measured cross sections in different phase-space regions are sensitive to different nuclear effects. Therefore, they enable the impact of specific nuclear effects on the neutrino-nucleus interaction to be isolated more completely than was possible using previous single-differential cross section measurements. Our results provide precision data to help test and improve neutrino-nucleus interaction models. They further support ongoing neutrino-oscillation studies by establishing phase-space regions where precise reaction modeling has already been achieved.