We demonstrate the strong coupling of a quantum dot and a graphene spherical shell coating it. Our simulations are based on solutions of three-dimensional Maxwell equations, using a boundary element method approach. Interaction between the nanostructures produces sharp hybrid modes, even when the two are off-resonant. The coupling of the light to these "very sharp" plexcitonic resonances is an order of magnitude larger than its coupling to a quantum dot, and they are voltage tunable (continuously) in an 80-meV interval. Hence, our results are very attractive for sensing applications and graphene display technologies with sharper colors. Moreover, on a simple theoretical model, we explain why such sharp highly tunable hybrid resonances emerge.