We formulate a drift-kinetic theory of electron phase-space vortices in magnetized space plasmas. It provides the theoretical explanation for the spatial and temporal scales of the electrostatic bipolar structures that have been observed by the Geotail and FAST spacecrafts in Earth's magnetotail and in the auroral zone. Our new nonlinear model accounts for the effects of both the electron polarization and the anisotropic electron temperature. Several different types of quasi-three-dimensional electron holes are found in the form of either cylinders or ellipsoids. Although topologically different, they produce similar signals on the spacecraft under typical FAST and Geotail observational conditions and cannot be distinguished with the use of the existing scarce satellite observational data.