  We consider reflection-asymmetric thin-shell wormholes within Palatini
$f(\mathcal{R})$ gravity using a matching procedure of two patches of
electrovacuum space-times at a hypersurface (the shell) via suitable junction
conditions. The conditions for having (linearly) stable wormholes supported by
positive-energy matter sources are determined. We also identify some subsets of
parameters able to locate the shell radius above the event horizon (when
present) but below the photon sphere (on both sides). We illustrate with an
specific example that such two photon spheres allow an observer on one of the
sides of the wormhole to see another (circular) shadow in addition to the one
generated by its own photon sphere, which is due to the photons passing above
the maximum of the effective potential on its side and bouncing back across the
throat due to a higher effective potential on the other side. We finally
comment on the capability of these double shadows to seek for traces of new
gravitational physics beyond that described by General Relativity.
