Drain the fava beans and place in a large saucepan. Add enough water to cover the beans. Cover the pot, and cook over medium-high heat. Skim the foam that rises to the top once the water boils. Once there is no more foam, add a generous pinch of salt and cook the beans, stirring occasionally, for about 1 hour, or until they have dissolved into the water and have taken the consistency of clotted cream. You may have to add more boiling water to keep beans from scorching. Using a hand-held electric mixer, beat in 1/4 cup olive oil and adjust the seasoning with salt and pepper, to taste. Transfer to a serving bowl.
While the beans cook, rinse the greens in water, then place them in a large saucepan over high heat and cook them, in the water that clings to their leaves, adding a little more water, if necessary, to prevent scorching. Once they are very tender, remove from the pan to a strainer and squeeze out excess water. Place in a serving dish and toss with the remaining 1/4 cup of olive oil and salt and pepper, to taste.
Serve the greens and fava puree together with the bread.