  We exhibit a concrete procedure to construct Einstein pseudo-K\"ahler and
para-K\"ahler metrics on solvable Lie algebras. We apply this method to
classify all the rank-one pseudo-Iwasawa extensions of type-(Nil4) nilsoliton
in low dimension. We prove that such metrics exists on the rank-one
pseudo-Iwasawa extension of the generalized Heisenberg Lie algebra.
  Further ideas and suggestions to produce more special Einstein
pseudo-Riemannian metrics are exposed.
