In a 4- to 5-quart Dutch oven combine potatoes, olives, the water, and shallots. Sprinkle with salt and pepper.
Bring to boiling; reduce heat. Simmer, covered, about 5 minutes or until potatoes are nearly tender. Stir in green beans. Simmer, covered, for 3 to 5 minutes more or until potatoes are tender and beans are crisp-tender, adding tomatoes for the last 1 minute of cooking.
Using a slotted spoon, transfer vegetables to individual rimmed plates or a rimmed serving platter. Drizzle with oil and lemon juice; sprinkle with parsley. If desired, garnish with hard-cooked eggs.