  We propose a mechanism to generate Primordial Black Holes (PBHs) which is
independent of cosmological inflation and occurs slightly below the QCD phase
transition. Our setup relies on the collapse of long-lived string-domain wall
networks and is naturally realized in QCD axion models with domain wall number
$N_{DW}>1$ and Peccei-Quinn symmetry broken after inflation. In our framework,
dark matter is mostly composed of axions in the meV mass range along with a
small fraction, $\Omega_{\text{PBH}} \gtrsim 10^{-6} \Omega_{\text{CDM}} $ of
heavy $M \sim 10^4-10^7 M_\odot$ PBHs. The latter could play a role in
alleviating some of the shortcomings of the $\Lambda$CDM model on sub-galactic
scales. The scenario has distinct signatures in ongoing axion searches as well
as gravitational wave observatories.
