Recrystallization of bulk materials is a well-known phenomenon, which is widely used in commercial manufacturing. However, for low-dimensional materials like graphene, this process still remains an unresolved puzzle. Thus, the understanding of the underlying mechanisms and the required conditions for recrystallization in low dimensions is essential for the elaboration of routes towards the inexpensive and reliable production of high-quality nanomaterials. Here, we unveil the details of the efficient recrystallization of one-atom-thick pure and boron-doped polycrystalline graphene layers on a Co(0001) surface. By applying photoemission and electron diffraction, we show how more than 90% of the initially misoriented graphene grains can be reconstructed into a well-oriented and single-crystalline layer. The obtained recrystallized graphene/Co interface exhibits high structural quality with a pronounced sublattice asymmetry, which is important for achieving an unbalanced sublattice doping of graphene. By exploring the kinetics of recrystallization for native and B-doped graphene on Co, we were able to estimate the activation energy and propose a mechanism of this process.