  Pionless effective field theory in a finite volume (FVEFT$_{\pi\!/}$) is
investigated as a framework for the analysis of multi-nucleon spectra and
matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{\pi\!/}$
with the stochastic variational method, the spectra of nuclei with atomic
number $A\in\{2,3\}$ are matched to existing finite-volume LQCD calculations at
heavier-than-physical quark masses corresponding to a pion mass $m_\pi=806$
MeV, thereby enabling infinite-volume binding energies to be determined using
infinite-volume variational calculations. Based on the variational
wavefunctions that are constructed in this approach, the finite-volume matrix
elements of various local operators are computed in FVEFT$_{\pi\!/}$ and
matched to LQCD calculations of the corresponding QCD operators in the same
volume, thereby determining the relevant one and two-body EFT counterterms and
enabling an extrapolation of the LQCD matrix elements to infinite volume. As
examples, the scalar, tensor, and axial matrix elements are considered, as well
as the magnetic moments and the isovector longitudinal momentum fraction.
