Remove the artichokes from the stems, which you will set aside, and the tougher outer leaves, cut them in half to remove the thorns, then cut them in half again, remove any hay and cut them in half again.
Also peel the stems and cut them into pieces about 3-4 centimeters long.
As you go, immerse both the cloves and the artichoke stems in a bowl full of water acidulated with the juice of a lemon.
Heat three tablespoons of olive oil in a saucepan.
Add the garlic cloves, the artichokes and their stems, well drained, and brown them over moderate heat for 5 minutes.
At this point, remove the garlic and put the diced cooked ham in the saucepan, let it flavor all together for two minutes, then wet the preparation with a ladle of broth and sprinkle it with the necessary salt and a grind of pepper.
Lower the flame to a minimum and continue cooking for 30 minutes, covered, being careful to stir occasionally and to add, if the cooking liquid tends to dry out excessively, a little more hot broth.
After the indicated time, when the artichokes have become tender, sprinkle them with chopped parsley, leave them on the heat for another couple of minutes, then turn off the heat and transfer them to a hot serving dish.
Pour the cooking liquid over the vegetables and serve.
Notes
Add some grated cheese on top of the artichokes before serving for an extra flavor kick.