  In this paper we look at ergodic BSDEs in the case where the forward dynamics
are given by the solution to a non-autonomous (time-periodic coefficients)
Ornstein-Uhlenbeck SDE with L\'evy noise, taking values in a separable Hilbert
space. We establish the existence of a unique bounded solution to an infinite
horizon discounted BSDE. We then use the vanishing discount approach, together
with coupling techniques, to obtain a Markovian solution to the EBSDE. We also
prove uniqueness under certain growth conditions. Applications are then given,
in particular to risk-averse ergodic optimal control and power plant evaluation
under uncertainty.
