Heat the olive oil in a large pot over medium heat. Add the onion, carrots, celery, kale stems, cumin, salt, and several grinds of pepper, and cook, stirring occasionally, for 8 minutes, or until the vegetables begin to soften.
Stir in the garlic, tomatoes, lentils, vinegar, thyme, and broth. Cover and simmer for 25 to 30 minutes, or until the lentils are tender. Add the kale leaves and cook for 5 minutes, or until wilted.
Remove the thyme bundle and season to taste. Serve topped with the parsley, red pepper flakes, and Parmesan, if desired.