Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onions, carrots, and celery. Stir frequently and cook for 8 to 10 minutes. You want the vegetables to soften and the onions to become translucent. Now, add the tomato paste, stirring it into the vegetables. Continue to cook for another 1-2 minutes until the paste darkens slightly. This step caramelizes the tomato paste, removing its raw taste and creating a much deeper flavor.
Stir in the minced garlic, ground fennel, black pepper, salt, and optional crushed red pepper flakes. Cook for about 1 minute, stirring constantly, until the garlic is fragrant. This process, known as "blooming," gently toasts the spices in the hot oil, which helps release their essential oils and intensifies their flavor and aroma.
Pour in the diced tomatoes with their juices, using a wooden spoon to scrape up any browned bits from the bottom of the pot (this is called deglazing, and it adds a ton of flavor). Stir well, then pour in the vegetable or chicken broth. Ensure the tomato paste is fully dissolved into the liquid.
Add the chopped potatoes, shredded cabbage, and the two bay leaves to the pot. Increase the heat to medium-high and bring the soup to a gentle boil. Once it's bubbling, reduce the heat to low, partially cover the pot with a lid, and let it maintain a steady simmer. Cook for 20 minutes, stirring occasionally, until the potatoes are tender enough to be easily pierced with a fork.
Stir in the frozen peas and continue to simmer for another 5 minutes. Since the peas are small and were frozen, they cook very quickly. Remove the pot from the heat and fish out the bay leaves to discard them. Stir in the optional apple cider vinegar or lemon juice. This final touch of acid will brighten the entire soup and make the vegetable flavors pop.
Taste the soup one last time and adjust the seasoning if needed with more salt, pepper, or a tiny bit more vinegar. Ladle the soup into bowls and serve hot. It pairs wonderfully with crusty bread for dipping, a side salad, or a sprinkle of fresh parsley.