Coherent wake emission may be generated only by sufficiently high-contrast driving laser pulses. When the laser contrast is too low, the formed long-scale-length plasma cannot support its generation. In this Letter, we show how, by gently spoiling a pristine laser contrast in an engineered way, coherent wake emission becomes inhibited in the center of the irradiated substrate only, thus forming an annular-shaped source of coherent extreme ultraviolet (XUV) pulses. We present an analytical model that describes the phenomenon and validation of its predictions in the experiment and the simulation. We also show how the ion-acoustic velocity dependency on the laser intensity may be obtained from the emission patterns and offer examples for future applications.