In a large pot or Dutch oven, heat the oil over medium. Add the leek, carrots and celery and cook, stirring occasionally, until the vegetables are tender-crisp.
Add the garlic, Italian seasoning, crushed red pepper, 1 teaspoon salt (or 1 ½ teaspoons if you’re using low-sodium broth) and ½ teaspoon black pepper; cook until the garlic is fragrant, 1 minute.
Add the potatoes and tomato paste and cook, stirring often, until the paste is fully incorporated and begins to brown on the bottom of the pot, 2 to 3 minutes.
Pour in the broth and diced tomatoes (with their juices) and bring to a simmer over medium-high heat.
Stir in the cabbage, lower the heat and simmer, partially covered and stirring occasionally, until the potatoes are fork tender, 20 to 25 minutes.
Off the heat, add the vinegar and parsley. Taste and add more salt and pepper, if necessary. Serve hot, topped with more parsley.
