Heat the oil in a large pot over medium heat. Add the onion, ½ teaspoon salt, and several grinds of pepper, and cook, stirring occasionally, for 8 minutes. Add the carrot and sweet potato, stir and cook 2 more minutes.
Add the wine and cook for about 30 seconds to reduce by half, then add the canned tomatoes, garlic, oregano, and red pepper flakes. Stir in the broth and bay leaves. Bring to a boil, then reduce the heat to a simmer and cook, covered, for 20 minutes.
Stir in the cherry tomatoes, green beans, zucchini, chickpeas, and cover and cook 10 to 15 more minutes, until the green beans are tender.
Stir in the vinegar, kale, an additional ½ teaspoon salt (or to taste), and more pepper.