Heat the oil in a large pot over medium heat. Add the onion, carrots, fennel, salt, and a few grinds of black pepper and cook, stirring, until the vegetables begin to soften, about 8 minutes.
Add the balsamic vinegar, garlic, tomatoes, broth, thyme, and red pepper flakes. Cover and simmer for 30 minutes, or until the vegetables are tender.
Meanwhile, cook the tortellini in a pot of salted boiling water according to the package directions until al dente. Add the tortellini and the kale to the soup and simmer for 2 more minutes.
Season to taste with about ¼ to ½ teaspoon more salt and a few generous grinds of pepper.
Serve in bowls with scoops of the kale pesto and sprinkle with fresh parsley.