  We consider the complexity of a single-sided AdS black hole as modelled by an
end-of-the-world brane. In addition, we present multi-boundary partition
functions and matter correlation functions for such a setting. We compute the
complexity using a modified replica trick corresponding to the "quenched
geodesic length" in JT gravity. The late-time behaviour of complexity shows a
saturation to a constant value of order $e^{S_0}$ following a period of linear
growth. Furthermore, we show that our approach leads to an improved result for
the variance of complexity, namely it being time-independent at late times. We
conclude by commenting on the introduction of dynamical end-of-the-world
branes.
