  We prove that for any winding number $m>0$ pattern $P$ and winding number
$-m$ pattern $Q$, there exist knots $K$ such that the minimal genus of a
cobordism between $P(K)$ and $Q(K)$ is arbitrarily large. This answers a
question posed by Cochran-Harvey [CH17] and generalizes a result of
Kim-Livingston [KL05].
