  We investigate the two-stage inflation regime in the theory of hybrid
cosmological $\alpha$-attractors. The spectrum of inflationary perturbations is
compatible with the latest Planck/BICEP/Keck results, thanks to the attractor
properties of the model. However, at smaller scales, it may have a very high
peak of controllable width and position, leading to a copious production of
primordial black holes (PBH) and generation of a stochastic background of
gravitational waves (SGWB).
