We investigate the maximum coding rate achievableon a two-user broadcast channel for the case where a common-message is transmitted using fixed-blocklength codes with feed-back. Specifically, we focus on a family of broadcast channels com-posed of two antisymmetric Z-channels. For this setup, we obtainmatching upper and lower bounds on the dispersion term in theasymptotic expansion of the maximum coding rate. These boundsreveal that the dispersion is halved compared to the no-feedbackcase