  Roughly half of the quasi-periodic eruption (QPE) sources in galactic nuclei
exhibit a remarkably regular alternating "long-short'' pattern of recurrence
times between consecutive flares. We show that a main-sequence star (brought
into the nucleus as an extreme mass-ratio inspiral; EMRI) which passes twice
per orbit through the accretion disk of the supermassive black-hole (SMBH) on a
mildly eccentric inclined orbit, each time shocking and ejecting
optically-thick gas clouds above and below the midplane, naturally reproduces
observed properties of QPE flares. Inefficient photon production in the ejecta
renders the QPE emission much harder than the blackbody temperature, enabling
the flares to stick out from the softer quiescent disk spectrum. Destruction of
the star via mass ablation limits the QPE lifetime to decades, precluding a
long-lived AGN as the gaseous disk. By contrast, a tidal disruption event (TDE)
naturally provides a transient gaseous disk on the requisite radial scale, with
a rate exceeding the EMRI inward migration rate, suggesting that many TDEs
should host a QPE. This picture is consistent with the X-ray TDE observed
several years prior to the QPE appearance from GSN 069. Remarkably, a second
TDE-like flare was observed from this event, starting immediately after
detectable QPE activity ceased; this event could plausibly result from the
(partial or complete) destruction of the QPE-generating star triggered by
runaway mass-loss, though other explanations cannot be excluded. Our model can
also be applied to black hole-disk collisions, such as those invoked in the
context of the candidate SMBH binary OJ 287.
