A drift-kinetic theory for electron phase-space vortices in magnetized space plasmas is formulated in the frequency range of lower-hybrid waves excited by the Buneman instability in the presence of an electron beam. The nonlinear model accounts for the effects of the electron polarization, anisotropic electron temperature and ion mobility, and it provides a theoretical explanation for some of the electrostatic and weakly electromagnetic bipolar structures observed by the Cluster, Polar and FAST spacecrafts in the Earth's magnetosheath, magnetopause and in the auroral zone. Quasi-3-D electron holes have the form of either elongated cylinders oblique to the magnetic field, or spheroids.