Fill a large bowl with cold water and juice the lemon into it. Set aside.
Clean the artichoke by pulling the outside leaves until you get to the very tender ones.
Cut the tips with a serrated knife, about 1-inch from the top.
With the help of a sharp knife trim the bottom part around the heart.
Cut the artichokes into quarters and transfer immediately to the lemon water.
Slice one of the artichokes lengthwise to 1/4-inch and grill it. Set aside.
In a large skillet sauté the shallots on medium-high until tender and translucent.
Add the smashed garlic cloves and stir for an additional minute.
Transfer the artichokes to the skillet add the fava beans and salt and pepper.
Stir to combine, add the vegetable stock and bring it to a simmer.
Cover and lower the heat to medium-low.
Cook for 15 to 20 minutes or until the artichokes and fava beans are tender and cooked through.
Bring a large pot of salted water to a boil.
Add the fresh Pappardelle and cook, stirring occasionally, for 3 minutes. Drain, reserving 1/2 cup pasta water.
Transfer the pasta to the artichoke sauce and toss. Stir in some of the reserved pasta water if sauce looks dry. Add the prosciutto and transfer to a warm serving plate. Top with Parmigiano-Reggiano.