Warm the oil in a large pot or Dutch oven set over medium heat. Add the onions and cook, stirring often, until soft but not brown, about 8 minutes.
Stir in the green beans, potatoes, zucchini, tomatoes, corn, eggplant, and salt. Put the long peppers on top. Pour 2 cups vegetable broth over the vegetables.
Bring to a simmer, then reduce the heat to low, cover, and cook, shaking the pan frequently without stirring, until the vegetables are tender, about 45 minutes.
Drizzle with olive oil as a garnish to serve.
