  We study monomial-Cartesian codes (MCCs) which can be regarded as
$(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural
bound for their minimum distance and we determine those giving rise to
$(r,\delta)$-optimal LRCs for that distance, which are in fact
$(r,\delta)$-optimal. A large subfamily of MCCs admits subfield-subcodes with
the same parameters of certain optimal MCCs but over smaller supporting fields.
This fact allows us to determine infinitely many sets of new
$(r,\delta)$-optimal LRCs and their parameters.
