How to Make It
In a medium saucepan of boiling water, blanch the fava beans until barely tender, about 2 minutes; reserve 1 cup of the cooking water. Drain and cool under cold running water, then peel the beans. Set aside 1/3 cup for garnish. Transfer the remaining beans to a food processor. Add 1/2 cup of the reserved cooking water and puree until smooth, adding more water as necessary to reach a smooth consistency. Season with salt and pepper. Scrape the fava puree into a small bowl and keep warm.
Preheat the oven to 350°. Season the lamb with salt and pepper. In a large ovenproof skillet, heat the olive oil with 1 tablespoon of butter. Add the lamb and cook, turning once, until browned, 2 to 3 minutes per side. Transfer the skillet to the oven and cook the lamb for about 5 minutes longer, until a thermometer inserted in the thickest part registers 125° for medium-rare. Transfer the lamb to a work surface and let stand for 5 minutes.
Meanwhile, in a medium saucepan, heat the remaining 2 tablespoons of butter until the foam subsides. Add the carrots and chicken stock and cook over moderate heat, stirring occasionally, until the carrots begin to soften, 3 to 5 minutes. Add the peas and cook until just warmed through, about 3 minutes. Remove the saucepan from the heat, stir in the chopped mint and season with salt and pepper. Spoon any lamb juices from the skillet into the peas.
Spoon the fava puree onto 4 plates. Thinly slice the lamb across the grain and transfer to the plates along with the carrots and peas in their sauce. Top with the reserved fava beans and mint leaves and serve.