One of the enduring challenges in graphene research and applications is the extreme sensitivity of its charge carriers to external perturbations, especially those introduced by the substrate. The best available substrates to date, graphite and hBN, still pose limitations: graphite being metallic does not allow gating, while both hBN and graphite having lattice structures closely matched to that of graphene, may cause significant band structure reconstruction. Here we show that the atomically smooth surface of exfoliated MoS2 provides access to the intrinsic electronic structure of graphene without these drawbacks. Using scanning tunneling microscopy and Landau-level spectroscopy in a device configuration which allows tuning the carrier concentration, we find that graphene on MoS2 is ultra-flat producing long mean free paths, while avoiding band structure reconstruction. Importantly, the screening of the MoS2 substrate can be tuned by changing the position of the Fermi energy with relatively low gate voltages. We show that shifting the Fermi energy from the gap to the edge of the conduction band gives rise to enhanced screening and to a substantial increase in the mean-free-path and quasiparticle lifetime. MoS2 substrates thus provide unique opportunities to access the intrinsic electronic properties of graphene and to study in situ the effects of screening on electron-electron interactions and transport.