Cut carrots into 1/2-inch-thick slices. Cut beans into 1 1/2-inch pieces. Cut the cauliflower into 1 1/2-inch florets. Cut pepper and peaches into 1-inch pieces.
In a 5- to 6-quart pan over medium-high heat, stir oil, onion, ginger, garlic, and cinnamon sticks until onion is limp, 5 to 7 minutes. Add curry powder and turmeric; stir 30 seconds. Add broth, carrots, beans, cauliflower, bell pepper, peaches, and cabbage; bring to a boil over high heat.
Cover and simmer over low heat, stirring occasionally, until carrots are tender when pierced, 20 to 25 minutes. Add salt to taste.