Heat the olive oil in a large skillet over medium-high heat. Add the diced onion and sauté for about 1 minute, until it begins to soften.
2 tbsp Olive oil, 1 medium Onion, diced
Add the shredded carrots and sliced mushrooms. Cook for 3–4 minutes, stirring occasionally, until the mushrooms release their liquid and start to brown.
2 small Carrots, shredded, 8 oz Mushrooms, sliced
Add the sliced cabbage. Stir well, then reduce the heat to medium, cover with a lid, and cook for about 15 minutes, or until the cabbage is tender but not mushy, stirring once or twice.
1 small head Green cabbage, thinly sliced
Stir in the tomato paste, apple cider vinegar, salt, and black pepper. Mix everything thoroughly and cook for another minute so the flavors come together.
1 tbsp Tomato paste, 1 tbsp Apple cider vinegar, ¾ tsp Sea salt, or to taste, ¼ tsp Black pepper, or to taste
Turn off the heat and sprinkle with chopped dill before serving.