  We present the discovery and extensive follow-up of a remarkable
fast-evolving optical transient, AT2022aedm, detected by the Asteroid
Terrestrial impact Last Alert Survey (ATLAS). AT2022aedm exhibited a rise time
of $9\pm1$ days in the ATLAS $o$-band, reaching a luminous peak with
$M_g\approx-22$ mag. It faded by 2 magnitudes in $g$-band during the next 15
days. These timescales are consistent with other rapidly evolving transients,
though the luminosity is extreme. Most surprisingly, the host galaxy is a
massive elliptical with negligible current star formation. X-ray and radio
observations rule out a relativistic AT2018cow-like explosion. A spectrum in
the first few days after explosion showed short-lived He II emission resembling
young core-collapse supernovae, but obvious broad supernova features never
developed; later spectra showed only a fast-cooling continuum and narrow,
blue-shifted absorption lines, possibly arising in a wind with $v\approx2700$
km s$^{-1}$. We identify two further transients in the literature (Dougie in
particular, as well as AT2020bot) that share similarities in their
luminosities, timescales, colour evolution and largely featureless spectra, and
propose that these may constitute a new class of transients: luminous
fast-coolers (LFCs). All three events occurred in passive galaxies at offsets
of $\sim4-10$ kpc from the nucleus, posing a challenge for progenitor models
involving massive stars or massive black holes. The light curves and spectra
appear to be consistent with shock breakout emission, though usually this
mechanism is associated with core-collapse supernovae. The encounter of a star
with a stellar mass black hole may provide a promising alternative explanation.
