We propose a model of two-stage inflation in which a scalar field, χχ, is non-minimally coupled to Starobinsky’s R2R2 gravity. The scalaron, ϕϕ, in Starobinsky’ model drives the first stage of inflation, and χχ drives the second. At the end of the first stage, the scalaron becomes heavy and undergoes damped oscillations. This causes enhancement and oscillatory features in the curvature perturbation power spectrum. The peak in these features may give rise to copious production of primordial black holes (PBHs). For a suitably chosen set of model parameters, these PBHs may even dominate the CDM of the Universe.