Cavity design is crucial for single-mode semiconductor lasers such as the ubiquitous distributed feedback and vertical-cavity surface-emitting lasers. By recognizing that both of these optical resonators feature a single mid-gap mode localized at a topological defect in the one-dimensional lattice, we upgrade this topological cavity design concept into two dimensions using a honeycomb photonic crystal with a vortex Dirac gap by applying the generalized Kekulé modulations. We theoretically predict and experimentally show on a silicon-on-insulator platform that the Dirac-vortex cavities have scalable mode areas, arbitrary mode degeneracies, vector-beam vertical emission and compatibility with high-index substrates. Moreover, we demonstrate the unprecedentedly large free spectral range, which defies the universal inverse relation between resonance spacing and resonator size. We believe that our topological micro-resonator will be especially useful in applications where single-mode behaviour is required over a large area, such as the photonic-crystal surface-emitting laser.