  We use holography to compute the large-$N$ effective field theory along the
moduli space of vacua of an infinite class of three-dimensional $\mathcal{N}=2$
SCFTs admitting a dual M-theory description. We focus in particular on toric
models and show how the spectrum of large $R$-charge SCFT chiral scalar
operators corresponds to a set of explicit semiclassical solutions of our
effective field theory, which describe bound states of backreacting giant
gravitons and baryonic-like M5-branes. Our semiclassical description allows for
a direct computation of the scaling dimensions of these operators and provides
a starting point for a semiclassical investigation of the SCFT data in the
large $R$-charge sector. We consider the models corresponding to the
$Y^{12}(\mathbb{P}^2)$ and $Q^{111}$ Sasaki-Einstein spaces as explicit
examples.
