In a large skillet over medium heat, add 1 tablespoon oil. Then add onion, carrots, and celery, and saute for 5 minutes, stirring occasionally. Transfer veggie mixture to large slow cooker.
Add another 1 tablespoon oil to same skillet, then add contents of can of tomatoes and garlic. Cook for about 3 minutes, while breaking up the tomatoes into small pieces. Transfer tomato mixture to slow cooker.
Add the kale, beans, broth, thyme, Italian seasoning, bay leaf, 1/2 teaspoon salt, 1/2 teaspoon pepper to the slow cooker, stir, then cook 6-7 hours on low, or about 4 hours on high, until veggies are tender.
Remove bay leaf. Stir in the vinegar. Season with additional salt and pepper, to taste, and serve.
Instant Pot
Saute onion, carrots, and celery in the Instant Pot on saute setting, about 5 minutes. Add the tomatoes and garlic and saute another 3 minutes or so.
Add the kale, beans, broth, thyme, Italian seasoning, bay leaf, 1/2 teaspoon salt, 1/2 teaspoon pepper to the pot and stir. Press the manual button and cook high pressure for 6 minutes, then let naturally release for 5-10 minutes.
Remove bay leaf. Stir in the vinegar. Season with additional salt and pepper, to taste, and serve.