  Slow first-order phase transitions generate large inhomogeneities that can
lead to the formation of primordial black holes (PBHs). We show that the
gravitational wave (GW) spectrum then consists of a primary component sourced
by bubble collisions and a secondary one induced by large perturbations. The
latter gives the dominant peak if $\beta/H_0 < 12$, impacting, in particular,
the interpretation of the recent PTA data. The GW signal associated with a
particular PBH population is stronger than in typical scenarios because of a
negative non-Gaussianity of the perturbations and it has a distinguishable
shape with two peaks.
