Cut the leek lengthwise. Discard the tough dark green leaves and slice the white and pale green parts of leek. Place and wash them in a bowl of cold water. All all the grit to fall to the bottom of the bowl, and using your hands scoop out the leeks and place them on a tea towel to drain.
Heat up the olive oil in a large enameled cast iron pot on low flame. Add the cleaned leeks with a pinch of sea salt and sauté for about 20 minutes until they start to caramelize.
Stir in the caraway seeds and toss to coat in the oils. Add the ground chicken or Italian sausage to the pot and break it up with the flat side of a wooden spoon. Cook for a few minutes then stir in the fresh cabbage. Cook on low for a few minutes until it starts to wilt.
Add the sauerkraut to the pot together with the peppercorns, San Marzano tomatoes with the puree or Passata, and half of the fresh dill. Use the wooden spoon to break up the tomatoes If they are whole.
Season with the sea salt and cover with the filtered water. Bring to a simmer and cover with a tight lid. Cook together for 20 minutes.
After 20 minutes have passed taste for seasonings, stir in the rice, cover with the lid and cook on low for another 15 minutes. Remove from heat and allow it to sit covered for 10 minutes.
Serve warm with sour cream on top, a drizzle of olive oil and sprinkled with fresh dill and freshly cracked black pepper.