It has been shown recently that atomically coherent superstructures of a nanocrystal monolayer in thickness can be prepared by self-assembly of monodisperse PbSe nanocrystals, followed by oriented attachment. Superstructures with a honeycomb nanogeometry are of special interest, as theory has shown that they are regular 2-D semiconductors, but with the highest valence and lowest conduction bands being Dirac-type, that is, with a linear energy-momentum relation around the K-points in the zone. Experimental validation will require cryogenic measurements on single sheets of these nanocrystal monolayer superstructures. Here, we show that we can incorporate these fragile superstructures into a transistor device with electrolyte gating, control the electron density, and measure the electron transport characteristics at room temperature. The electron mobility is 1.5 ± 0.5 cm² V^-1 s^-1, similar to the mobility observed with terahertz spectroscopy on freestanding superstructures. The terahertz spectroscopic data point to pronounced carrier scattering on crystallographic imperfections in the superstructure, explaining the limited mobility.