Heat olive oil in a skillet over medium heat. Saute the onion for 2-3 minutes, stirring occasionally. Then, add the carrots and saute for an additional 3 minutes. Next, add the cabbage and saute for 5 minutes, stirring occasionally.
Push the cabbage to the edges of the skillet to create a well in the middle. Add the tomato paste and cook for 1 minute until it begins to caramelize. Then, sprinkle in salt, pepper, and sugar, stirring everything together.
Pour in water and reduce the heat to low. Braise the mixture for 25 minutes, stirring every 5 minutes. Cover the skillet with a lid during cooking.
Once done, garnish with fresh parsley and serve with a dollop of sour cream. Enjoy your flavorful sauteed cabbage dish!