Soak the beans overnight. (If you’re in a hurry, soak the beans for a few hours in hot water instead.)
Drain the beans and remove as much of their skins as possible. Place the beans in a pot with the chopped onion, water and salt and bring to a boil. Lower the heat to simmer and continue to cook for about an hour, until the beans are soft and most of the water is absorbed.
Transfer the bean mixture to a food processor and blend until smooth. Taste for salt and add more, if needed. Pour the mixture into a shallow baking dish and refrigerate for two or more hours until the mixture sets (it should be solid enough to cut).
Line a serving platter with the sliced red onions (if using), then cut the fava into 1½-inch squares and place on top of the onion slices. Drizzle with olive oil and lemon juice and garnish with the dill. Serve chilled.