  We construct time quasi-periodic vortex patch solutions with one hole for the
planar Euler equations. These structures are captured close to any annulus
provided that its modulus belongs to a massive Borel set. The proof is based on
Nash-Moser scheme and KAM theory applied with a Hamiltonian system governing
the radial deformations of the patch. Compared to the scalar case, some
technical issues emerge due to the interaction between the interfaces. One of
them is related to a new small divisor problem in the second order Melnikov
non-resonances condition coming from the transport equations advected with
different velocities.
