We report on a flux-integrated multi-differential measurement of charged-current muon neutrino scattering on argon with one muon and one proton in the final state using the Booster Neutrino Beam and MicroBooNE detector at Fermi National Accelerator Laboratory. The data are studied as a function of various kinematic imbalance variables and of a neutrino energy estimator, and are compared to a number of event generator predictions. We find that the measured cross sections in different phase-space regions are sensitive to nuclear effects. Our results provide precision data to test and improve the neutrino-nucleus interaction models needed to perform high-accuracy oscillation analyses. Specific regions of phase-space are identified where further model refinements are most needed.