Heat the olive oil in a large heavy-bottomed saucepan over medium heat. Add the onion and cook, stirring occasionally, for 5 minutes. Add the zucchinis, potatoes, garlic and chard and cook, stirring occasionally, for 5 minutes more until the greens have wilted.
Pour in the stock and water and bring everything to the boil. Reduce the heat to low and simmer for 20 minutes. Add in the Cannellini beans and simmer for another 20 minutes. Return the barley, green beans and peas, and simmer for a final 5 to 10 minutes, or until the vegetables are tender. Season with salt and pepper, and grate the Parmesan over the dish before serving.