  We reveal the existence of a new form of spontaneously scalarized black-hole
configurations. In particular, it is proved that Reissner-Nordstr\"om black
holes in the highly charged regime $Q/M>(Q/M)_{\text{crit}}=\sqrt{21}/5$ can
support {\it thin} matter shells that are made of massive scalar fields with a
non-minimal coupling to the Gauss-Bonnet invariant of the curved spacetime.
These static scalar shells, which become infinitesimally thin in the
dimensionless large-mass $M\mu\gg1$ regime, hover a finite proper distance
above the black-hole horizon [here $\{M,Q\}$ are respectively the mass and
electric charge of the central supporting black hole, and $\mu$ is the proper
mass of the supported scalar field]. In addition, we derive a remarkably
compact analytical formula for the discrete resonance spectrum
$\{\eta(Q/M,M\mu;n)\}_{n=0}^{n=\infty}$ of the non-trivial coupling parameter
which characterizes the bound-state
charged-black-hole-thin-massive-scalar-shell cloudy configurations of the
composed Einstein-Maxwell-scalar field theory.
