Vertical integration of hexagonal boron nitride (h-BN) and graphene for the fabrication of vertical field-effect transistors or tunneling diodes has stimulated intense interest recently due to the enhanced performance offered by combining an ultrathin dielectric with a semi-metallic system. Wafer scale fabrication and processing of these heterostructures is needed to make large scale integrated circuitry. In this work, by using remote discharged, radio-frequency plasma chemical vapor deposition, wafer scale, high quality few layer h-BN films are successfully grown. By using few layer h-BN films as top gate dielectric material, the plasmon energy of graphene can be tuned by electrostatic doping. An array of graphene/h-BN vertically stacked micrometer-sized disks is fabricated by lithography and transfer techniques, and infrared spectroscopy is used to observe the modes of tunable graphene plasmonic absorption as a function of the repeating (G/h-BN)(n) units in the vertical stack. Interestingly, the plasmonic resonances can be tuned to higher frequencies with increasing layer thickness of the disks, showing that such vertical stacking provides a viable strategy to provide wide window tuning of the plasmons beyond the limitation of the monolayer.