The popularity of the GW approximation to the self-energy to access the quasiparticle energies of molecules is constantly increasing. As the other methods addressing the electronic correlation, the GW self-energy unfortunately shows a very slow convergence with respect to the basis complexity, which precludes the calculation of accurate quasiparticle energies for large molecules. Here we propose a method to mitigate this issue that relies on two steps: (i) the definition of a reduced virtual orbital subspace, thanks to a much smaller basis set; (ii) the account of the remainder through the simpler one-ring approximation to the self-energy. We assess the quality of the corrected quasiparticle energies for simple molecules, and finally we show an application to large graphene chunks to demonstrate the numerical efficiency of the scheme.