  Endosplit $p$-permutation resolutions play an instrumental role in verifying
Brou\'{e}'s abelian defect group conjecture in numerous cases. In this article,
we give a complete classification of endosplit $p$-permutation resolutions and
reduce the question of Galois descent of an endosplit $p$-permutation
resolution to the Galois descent of the module it resolves. This is shown using
techniques from the study of endotrivial complexes, the invertible objects of
the bounded homotopy category of $p$-permutation modules. As an application, we
show that a refinement of Brou\'{e}'s conjecture proposed by Kessar and
Linckelmann holds for all blocks of $p$-solvable groups.
