In a large pot, heat a generous splash of olive oil over medium heat. Add the carrots and onions, sautéing until the onions become translucent and the carrots start to soften, about 5 minutes.
Stir in the garlic and cook for another minute until fragrant.
Add Beets and Cabbage:
Mix in the chopped beets and cabbage. Sauté for about 10 minutes, stirring occasionally, until the vegetables start to soften.
Incorporate Tomato Paste:
Add the tomato paste to the pot, stirring well to coat the vegetables evenly. Cook for 2-3 minutes.
Add Liquids and Simmer:
Pour in the vegetable stock, red wine vinegar, and apple cider vinegar. Season with salt and pepper to your liking.
Bring the mixture to a boil, then reduce the heat to low. Cover and let it simmer for about 30 minutes, or until the beets and carrots are tender.
Serve:
Taste and adjust seasoning if necessary.
Ladle the hot soup into bowls. Serve each bowl with a slice of bread (regular or gluten-free), a dollop of Greek yogurt, and a sprinkle of fresh fennel on top.