Graphene-based materials have been suggested for applications ranging from nanoelectronics to nanobiotechnology. However, the realization of graphene-based technologies will require large quantities of free-standing two-dimensional (2D) carbon materials with tunable physical and chemical properties. Bottom-up approaches via molecular self-assembly have great potential to fulfill this demand. Here, we report on the fabrication and characterization of graphene made by electron-radiation induced cross-linking of aromatic self-assembled monolayers (SAMs) and their subsequent annealing. In this process, the SAM is converted into a nanocrystalline graphene sheet with well-defined thickness and arbitrary dimensions. Electric transport data demonstrate that this transformation is accompanied by an insulator to metal transition that can be utilized to control electrical properties such as conductivity, electron mobility, and ambipolar electric field effect of the fabricated graphene sheets. The suggested route opens broad prospects toward the engineering of free-standing 2D carbon materials with tunable properties on various solid substrates and on holey substrates as suspended membranes.