Heat the Oil: In a large Dutch oven, warm the olive oil over medium-high heat.
Sauté the Vegetables: Add the chopped carrots, celery, and sweet onion to the pot. Cook for about 5 minutes, or until the vegetables begin to soften.
Add Seasonings: Stir in 1 teaspoon of salt, ¼ teaspoon of black pepper, and all the minced garlic. Cook for an additional minute until fragrant.
Incorporate the Cabbage: Add the chopped red cabbage to the pot and sauté for about 5 minutes, stirring frequently.
Combine with Broth: Carefully pour the vegetable broth over the cabbage mixture, then add the diced potato. Give it a gentle stir to ensure everything is submerged.
Simmer: Bring the soup to a simmer. Cover and cook for 20-30 minutes, or until all the vegetables are tender.
Finish the Soup: Remove from heat and stir in the red wine vinegar along with the remaining salt and pepper. Adjust the seasoning to taste.
Serve: Garnish with fresh parsley before serving.