Cabling strongly invertible knots induces an operator on associated 4-ended tangles. In the case of 2-cabling, I will describe the construction of the resulting operator on the bordered Khovanov theory of Koteslkiy–Watson–Zibrowius, a theory that assigns type D structures to 4-ended tangles. The construction of the operator makes substantial use of Bar-Natan's planar algebra structure on complexes of cobordisms. Finally, I will discuss some of the structure revealed by this operator, in particular, what it says about a new concordance invariant that is derived from Rasmussen's s-invariant, due to Lewark–Zibrowius.