Heat 2 tablespoons oil in a large pot or Dutch oven over medium-low.
Add 1 diced fennel bulb, 1 diced onion, 1 tablespoon minced garlic, ½ teaspoon salt, ½ teaspoon black pepper, and ¼ teaspoon red pepper flakes, and cook until softened, about 5 minutes.
Stir in 1 tablespoon minced oregano (or 2 teaspoons dried) and cook 30 seconds.
Stir in 2 (28-ounce) cans tomatoes with their juices and 6 cups broth, bring soup to a boil then reduce to a simmer and cook for 10 minutes.
Stir in 10 ounces chopped kale, simmer 10 minutes.
Stir in 1 can chickpeas and 2 tablespoons vinegar and simmer 5 minutes. Season soup with additional salt, pepper flakes, and vinegar to taste.
Drizzle servings with olive oil and top with chopped fennel fronds.