We investigate a model of R2-gravity with a non-minimally coupled scalar field that
gives rise to two-stage inflation with a break, that is, with an intermediate stage where
inflation momentarily halts. We find that the power spectrum of the primordial curvature
perturbation is significantly enhanced at the break scale, which can account for the primordial
black hole (PBH) formation, without affecting the CMB constraint on large scales. The behavior of
the curvature perturbation is carefully analyzed and we find a few notable new features in the
spectrum. In particular, we find that the k3 growth of the spectrum of toward the end of the
first stage of inflation. We argue that this is a universal feature common to all two-stage models
where the field dominating the second stage is heavy during the first stage. By appropriately
tuning the model parameters, we find that our model can realize the scenario of PBHs as the cold
dark matter of the Universe. We also find that we can choose the parameters so that the spectrum
of the induced gravitational waves from the enhanced curvature perturbation fits the NANOGrav-15yr
data of pulsar timing array observation.