Sorry, that the buns got into the garden. Those jerusalem artichokes sound neat.My fence wasn't tight enough, the kits got through - so I can tell you they love carrot tops (all gone), chives (also, they just left bare earth), and young cabbage. My gardening attempts are a desaster so far. They did nibble the beans, but there's something left of those. Pumpkin plants went untouched, but I feed pumpkin in winter.
If you have enough space, jerusalem artichokes are really great rabbit plants, I feed excess greens, they give shade in summer (up to 4m tall), and I harvest the tubers for me and the rabbits in Winter. They need to be protected from the buns until they are about 2ft, then it's a great place to spend the day.