Preheat the oven to 325°F.
Add the fava bean greens, lemon juice, and minced garlic to a small bowl. Season with salt and pepper, add the olive oil, and whisk to combine.
Place the artichokes, fava beans, and garlic in a small baking dish. Drizzle the fava bean greens mixture over the top. Sprinkle with a pinch of salt. Place in the oven and cook for 1 hour or until the vegetables are tender and soft. Remove from the oven.
Arrange the Parmigiano-Reggiano on a large plate. Place the vegetables on top of the cheese and squeeze a small amount of lemon juice over the top, if desired. Serve immediately.