  We develop a theory for manipulating the effective band structure of
interacting helical edge states realized on the boundary of two-dimensional
time-reversal symmetric topological insulators. For sufficiently strong
interaction, an interacting edge band gap develops, spontaneously breaking
time-reversal symmetry on the edge. The resulting spin texture, as well as the
energy of the the time-reversal breaking gaps, can be tuned by an external
moir\'e potential (i.e., a superlattice potential). Remarkably, we establish
that by tuning the strength and period of the potential, the interacting gaps
can be fully suppressed and interacting Dirac points re-emerge. In addition,
nearly flat bands can be created by the moir\'e potential with a sufficiently
long period. Our theory provides an unprecedented way to enhance the coherence
length of interacting helical edges by suppressing the interacting gap. The
implications of this finding for ongoing experiments on helical edge states is
discussed.
