Heat the oil in a heavy large stockpot over medium-high heat. Add the onions, celery, carrot, bell pepper, and garlic, and saute until the onions are translucent, about 15 minutes. Add the chili powder, coriander, cumin, oregano and crushed red pepper, and cook for 2 minutes. Stir in the tomatoes with their juices, tomato juice, tomato paste, cheese rind, and 2 teaspoons of salt. Add the broth, garbanzo beans, cannellini beans, and lentils. Stir in the broccoli, zucchini, and yellow squash. Bring to a simmer over high heat. Decrease the heat to medium. Simmer, uncovered, until the lentils are tender and the mixture thickens slightly, stirring often, about 20 minutes. Season the stew to taste with more salt, if desired.
Ladle the stew into bowls. Sprinkle with the shredded cheese and basil, and serve.