Cut out the core of the cabbage. Then thinly slice the cabbage into thin ribbons or strips. Peel the onions, slice in half and then thinly slice the onions into strips as well.
Heat olive oil in a saucepan. Add the finely sliced onion and sauté until transparent for about 5 minutes, stirring occasionally.
Add the sliced cabbage, coarsely chopped walnuts, chopped garlic, salt and pepper and continue to cook while stirring for another 5 minutes, until the cabbage is slightly reduced in volume.
Add the washed wild rice, vinegar and water. Mix well, cover and bring to a boil. Lower to low heat (but not the minimum heat - just low heat) and cook for 50-60 minutes. While cooking, stir the dish occasionally - if at some point the liquids run out, then you can add water up to a maximum of an additional half a cup of water. The stew is ready when the wild rice kernels are burst open and the water evaporate completely. Leave the pot covered for an additional 5 minutes after the end of cooking.
Sprinkle on the chopped parsley and serve. Store in the refrigerator in an airtight container for up to 3 days.