  First-order phase transitions, which take place when the symmetries are
predominantly broken (and masses are then generated) through radiative
corrections, produce observable gravitational waves and primordial black holes.
We provide a model-independent approach that is valid for large-enough
supercooling to quantitatively describe these phenomena in terms of few
parameters, which are computable once the model is specified. The validity of a
previously-proposed approach of this sort is extended here to a larger class of
theories. Among other things, we identify regions of the parameter space that
correspond to the background of gravitational waves recently detected by pulsar
timing arrays (NANOGrav, CPTA, EPTA, PPTA) and others that are either excluded
by the observing runs of LIGO and Virgo or within the reach of future
gravitational wave detectors. Furthermore, we find regions of the parameter
space where primordial black holes produced by large over-densities due to such
phase transitions can account for dark matter. Finally, it is shown how this
model-independent approach can be applied to specific cases, including a
phenomenological completion of the Standard Model with right-handed neutrinos
and gauged $B-L$ undergoing radiative symmetry breaking.
