How to Make It
Fill a large bowl with water. Squeeze the juice from the halved lemon into the water and add the lemon halves to the bowl. Working with 1 artichoke at a time, peel off all of the dark green outer leaves. Using a large, sharp knife, cut off the leaves just above the heart, then scoop out the choke. Peel the heart and stem and add the artichoke to the water.
In a large, deep skillet, heat 1 tablespoon of the olive oil. Add the onion, carrot, celery and garlic and cook over moderate heat, stirring occasionally, until just softened, about 5 minutes. Add the stock, wine and the remaining 1/2 cup of olive oil and bring to a simmer. Add the peppercorns, artichoke hearts and a generous pinch of salt. Cover and braise the artichokes over moderately low heat, turning once, until just tender, about 15 minutes. Using a slotted spoon, transfer the artichoke hearts to a plate. Let cool completely, then cut off and finely chop the stems. Discard the braising liquid.
Preheat the oven to 350°. Lightly oil a medium baking pan and arrange the artichoke hearts in it, cup side up. In a medium bowl, mix 1/2 cup of the panko with the chopped artichoke stems and the tomato, olives, garlic, oregano, marjoram, salt, pepper and 1 tablespoon of the Parmigiano. Gently stir in the beaten egg. In a small bowl, mix the remaining 2 tablespoons of panko with the remaining 1 tablespoon of Parmigiano. Spoon the stuffing into the artichoke hearts and top with the panko-cheese mixture and a drizzle of olive oil. Bake for about 25 minutes, until the artichokes are hot and browned on top. Transfer to plates and serve right away.