Cook the shelled fava beans in a pot of salted boiling water until they are just tender, about 4 minutes, depending on their size. Drain the beans and run them under cold water to stop the cooking process. Once the fava beans are cool enough to handle, gently press them between your fingers to pop the tender green centers out of the skins. Set the beans aside.
Meanwhile, heat the olive oil over medium heat in a large pot. Stir in the onions and diced ham and reduce the heat to low. Let the onions slowly cook, stirring occasionally, while you prepare the artichokes. Reduce the heat to very low if the onions begin to brown.
Fill a medium bowl with water and squeeze in the juice from the lemon. Clean and quarter the artichokes (here are some excellent instructions), dropping the quarters into the bowl to prevent browning. Since the stems are also delicious when cooked, I like to peel them and leave a 1- to 1 1/2-inch tail.
When the artichokes are ready, the onions should be soft and beginning to turn golden (it took me nearly 30 minutes to prepare the artichokes - I'm slow). Stir in half of the garlic and the artichoke quarters. Reduce the heat to low, partially cover the pot and cook, stirring occasionally, until the artichokes have begun to soften, about 10 minutes. Add another tablespoon of olive oil if the pot seems dry. Pour in the sherry and increase the heat to high. Cook the sherry for about 1 minute, allowing it to reduce slightly.
Add enough chicken broth to just cover the vegetables and bring the liquid to a simmer. Cook the stew over low heat, partially covered, until the artichokes are completely tender, about 20 to 30 minutes, depending on their size. Add more broth as needed to keep the artichokes barely covered. Once the artichokes are done, add the fava beans and cook until they are tender, about 5 more minutes.
Place the parsley and remaining garlic in a mortar and pound them into a paste using a pestle. A pinch of salt can help. Stir the paste into the stew and cook for another minute to allow the flavors to blend. Season with salt and pepper to taste and serve warm.