Remove the favas beans from their pods.
In a medium pot, bring 6 cups water to a boil and salt it. Prepare an ice water bath. Add the fava beans to the boiling water and cook briefly to loosen their skins, 30 seconds to 1 minute. Drain with a spider and add to the ice water to stop the cooking. Reserve the boiling water. Peel the skins from the fava beans.
Add the potato, carrot, celery and shallot to the boiling water. Season with some salt, reduce to a low boil and cook to flavor the broth until the potato is tender, about 30 minutes. Remove the potato, peel it under running water, and cut it into chunks. Set aside the carrot, celery, shallot and broth.
Add the fava beans, the potato and the vegetables from the broth to a food processor along with a ladleful of the broth. Season with some salt and pepper to taste. Blend until smooth, adding a little more broth if necessary. Add some extra-virgin olive oil to taste.
Season the scallops lightly on both sides with salt and pepper. Melt the butter and 1 tablespoon olive oil in a nonstick pan. Once foaming and hot, sear the scallops, about 3 minutes on each side. Do not move the scallops while they are searing or they might break.
Place a generous 2 tablespoons of fava puree in the center of each of 4 small plates. Place some seared scallops on top of each and garnish with a few mint leaves.