Brown the turkey in the oil over medium-high heat, breaking it into small pieces and letting it sit long enough to color.
Add the onion and carrot to the same pot and cook them down in the turkey fat until the onion softens and turns translucent.
Pile the cabbage in. It will look like far too much for the pot, and it collapses to half its height in about five minutes.
Pour in the tomatoes and the broth, scraping the brown bits up off the bottom, and bring the whole pot to a gentle simmer.
Simmer uncovered for 25 minutes, until the cabbage is tender and the broth has thickened, then stir the parsley through it.
