We demonstrate molecular beam growth of graphene on biotite mica substrates at temperatures below 1000{deg}C. As indicated by optical and atomic force microscopy, evaporation of carbon from a high purity solid-state source onto biotite surface results in the formation of single-, bi-, and multilayer graphene with size in the micrometer regime. Graphene grown directly on mica surface is of very high crystalline quality with the defect density below the threshold detectable by Raman spectroscopy. The interaction between graphene and the mica substrate is studied by comparison of the Raman spectroscopy and atomic force microscopy data with the corresponding results obtained for graphene flakes mechanically exfoliated onto biotite substrates. Experimental insights are combined with density functional theory calculations to propose a model for the initial stage of the van der Waals growth of graphene on mica surfaces. This work provides important hints on how the direct growth of high quality graphene on insulators can be realized in general without exceeding the thermal budget limitations of Si technologies.