Aromatic plants tend to be immune to pests. The pungent oils dissuade them from munching the leaves. However, for the last few years we've had these attractive looking creatures on our big rosemary bush, and they rather seem to like it. Most leaves have been at least a bit chewed. Last night I made a chorizo, lentil and sausage casserole which requires fresh chopped rosemary and I found many of these beetles. They have the prosaic name Rosemary Beetle and the best way to get rid of them is to spread newspaper under the bush and give it a big shake.