Primordial black holes (PBHs) can generically form in inflationary setups through the
collapse of enhanced cosmological perturbations, providing us access to the early Universe through
their associated observational signatures. In the current work we propose a new mechanism of PBH
production within non-canonical inflation, using a class of steep-deformed inflationary potentials
compatible with natural values for the non-canonical exponents. In particular, requiring
significant PBH production we extract constraints on the non-canonical exponents. Additionally, we
find that our scenario can lead to the formation of asteroid-mass PBHs, which can account for the
totality of the dark matter, as well as to production of solar-mass PBHs within the LIGO-VIRGO
detection band. Finally, we find that the enhanced cosmological perturbations which collapse to
form PBHs can produce a stochastic gravitational-wave (GW) background induced by second-order
gravitational interactions. Very interestingly, we obtain a GW signal detectable by future GW
experiments, in particular by SKA, LISA and BBO.