How to Make It
In a large saucepan, heat 2 tablespoons of the olive oil until shimmering. Add the onions and cook over moderately high heat, stirring, until softened, about 5 minutes. Add the drained fava beans, potato, water, sugar, 2 tablespoons of the lemon juice and 1 teaspoon of salt and bring to a boil. Cover partially and cook over moderately low heat until the fava beans and potato are broken down and the liquid is nearly absorbed, about 1 hour.
Transfer the mixture to a food processor and pulse until coarsely pureed. Season with salt, add 2 tablespoons of the dill and stir until incorporated. Transfer the puree to a serving bowl and let cool to room temperature.
Meanwhile, in a small bowl, whisk together the remaining 1/4 cup of olive oil, 1/4 cup of lemon juice and 2 tablespoons of dill. Season with salt and pour the dressing over the fava puree. Serve the puree with pita.