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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±1 days in the ATLAS o-band, reaching a luminous peak with Mg ≈ −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 ≈ 2700 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 ∼ 4 − 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.