  We propose a new scheme for constructing an effective-field-theory-based
interaction to be used in the energy-density-functional (EDF) theory with
specific assumptions for defining a power counting. This procedure is developed
through the evaluation of the equation of state (EOS) of symmetric and pure
neutron matter going beyond the mean-field scheme and using a functional
defined up to next-to-leading order (NLO), that we will call NLO EDF. A
Skyrme-like interaction is constructed based on the condition of
renormalizibility and on a power counting on $k_F/\Lambda_{hi}$, where $k_F$ is
the Fermi momentum and $\Lambda_{hi}$ is the breakdown scale of our expansion.
To absorb the divergences present in beyond mean-field diagrams, counter
interactions are introduced for the NLO EDF and determined through
renormalization conditions. In particular, three scenarios are explored and all
of them lead to satisfactory results. These counter interactions contain also
parameters which do not contribute to the EOS of matter and may eventually be
determined through future adjustments to properties of some selected finite
nuclei. Our work serves as a simple starting point for constructing a
well-defined power counting within the EDF framework.
