Prick the sausages and sauté them over medium heat in a bit of olive oil until lightly browned in a sauté pan or braiser. Remove them from the pan and set aside.

Add the sliced onion and let the onion sauté for a few minutes, lowering the heat if need be to prevent it from browning. (A few drops of water will help things along.) Then add your shredded cabbage and mix it well with the onion. Season well with salt and pepper. Continue cooking, stirring often, until the cabbage has reduced down quite a bit. (You can cover it between stirs, which allows it to steam in its own liquid, which quickens the process.)

When the cabbage has reduced in volume by about half, you can add some diced apple if you like, which gives the dish a slight sweetness. Stir again to mix the apple evenly into the cabbage. You can also add a few fennel seeds, which adds another layer of flavor.

Then add the sausages back into the pan, nestling them into the cabbage at even intervals, and pour in enough broth (or water) to almost cover the cabbage. Lower the heat, then cover the pan, and let the dish simmer for a good 45 minutes to an hour, until the cabbage is literally melting and the sausages are quite soft, too. If there is a lot of liquid left in the pan, raise the heat to high and boil it (almost completely) off.

Adjust for seasoning and serve immediately on a warmed platter or straight from the pan.