  We study a Majorana island coupled to a bulk superconductor via a Josephson
junction and to multiple external normal leads. In the absence of the Josephson
coupling, the system displays a topological Kondo state, which had been largely
studied recently. However, we find that this state is unstable even to small
Josephson coupling, which instead leads at low temperature $T$ to a new fixed
point. Most interesting is the case of three external leads, forming a minimal
electronic realization of the long sought two-channel Kondo effect. While the
$T=0$ conductance corresponds to simple resonant Andreev reflection, the
leading $T$ dependence forms an experimental fingerprint for non-Fermi liquid
properties.
