1. Bring a large saucepan of water to boil. Add the broad beans and 1/4 teaspoon of the salt and cook for 2 minutes. Drain and rinse immediately with cold water. To remove the skins, pinch each bean on the side opposite where it was attached to the pod; the bean should slip easily from the skin. Remove and discard the outer skins. Set the beans aside.
2. In large sauce pan sauté the onion in oil until soft and lightly golden, about 6 minutes. Add the garlic and sauté for 30 seconds; don't let the garlic brown. Add the broad beans and stock and bring to a boil. Reduce the heat to low, cover and simmer, shaking the pan gently from time to time, until the beans are tender, about 15 minutes.
3. Season with the remaining 1/4 teaspoon salt and the pepper. Sprinkle with the parsley and serve immediately.