  F. Block and L. G\"ottsche introduced refined tropical invariants of toric
surfaces that intertwine tropical Gromov-Witten and Welschinger invariants of
toric surfaces. L. G\"ottsche and the first author introduced refined broccoli
invariants that intertwine some genus zero descendant tropical invariants and
broccoli invariants of toric surfaces. In this note, we extend the refined
broccoli invariants to the genus one case.
