Add the water to a large, deep pan, place over high heat, and bring to a boil. Add the artichoke bottoms and fava beans, and add more water to cover them if necessary.

Bring back to a boil, then reduce the heat to medium-low, and add the salt, pepper, sugar, lemon, and garlic. Cover the pan and simmer gently for 30 minutes, until the vegetables are cooked through.

In a small bowl, combine the cornstarch with 3 tablespoons of cold water and beat with a fork, making sure the cornstarch is dissolved. Then add 2 tablespoons of the hot cooking liquid from the pan, and pour this mixture back into the pan, stirring vigorously so that the sauce does not become lumpy.

Stir in the dill and continue to simmer gently over low heat for about 10 minutes, until the sauce has thickened. Serve warm or cold.