  The simultaneous breaking of time-reversal and inversion symmetry, in
connection to superconductivity, leads to transport properties with disrupting
scientific and technological potential. Indeed, the anomalous Josephson effect
and the superconducting-diode effect hold promises to enlarge the technological
applications of superconductors and nanostructures in general. In this context,
the system we theoretically analyze is a Josephson junction (JJ) with coupled
reconstructed topological channels as a link; such channels are at the edges of
a two-dimensional topological insulator (2DTI). We find a robust $\varphi_0$
Josephson effect without requiring the presence of external magnetic fields.
Our results, which rely on a fully analytical analysis, are substantiated by
means of symmetry arguments: Our system breaks both time-reversal symmetry and
inversion symmetry. Moreover, the anomalous current increases as a function of
temperature. We interpret this surprising temperature dependence by means of
simple qualitative arguments based on Fermi's golden rule.
