  We study the formation of primordial black holes (PBHs) in strongly
supercooled first-order phase transitions. The mechanism is based on the
presence of remnants dominated by the false vacuum that scale slower with the
expansion of the Universe than their surroundings where this energy was already
converted into radiation. We compute the PBH formation from these remnants
including the contribution from the false vacuum and the bubble walls, by
estimating the collapse using the hoop conjecture and by considering both
regions collapsing immediately when entering the horizon and sub-horizon
regions that collapse as their compactness grows. We show that for exponential
bubble nucleation rate, $\Gamma \propto e^{\beta t}$, the primordial black hole
formation implies $\beta/H \gtrsim 3.8$, where $H$ denotes the Hubble rate, if
the potential energy of the false vacuum is $\Delta V \lesssim (10^{12} {\rm
GeV})^4$, as otherwise a too large abundance of long-lived PBHs forms. The
observed dark matter abundance can be formed in asteroid mass PBHs if $\beta/H
\simeq 3.8$ and $10^5 {\rm GeV} \lesssim \Delta V^{1/4} \lesssim 10^8 {\rm
GeV}$. Finally, we consider also the effect of the second order correction to
the exponential nucleation rate showing that the PBH abundance is mainly
determined by the average radius of the true vacuum bubbles.
