Heat oven to 425°F. Toss cauliflower, carrots and onion with 1 tablespoon oil, salt and pepper on a large rimmed sheet pan and roast for 20 minutes.
Toss zucchini and tomatoes with the remaining tablespoon oil. Add them to the pan, turn the firmer vegetables and roast for 12 to 15 minutes more until the cauliflower and carrots are tender and the tomatoes begin to burst.
Put broth, garlic, ham and oregano in a soup pot and bring to a gentle simmer while the vegetables finish.
Transfer roasted vegetables and their pan juices to the pot. Simmer gently for 5 to 7 minutes until the ham reaches 165°F, keeping the vegetables in recognizable pieces.
Remove from heat and stir in basil. Divide among six bowls, distributing the different vegetables and ham evenly.