Cut the pointy ends of the artichokes off with a pair of scissors. Cut off the tip of the stems and discard, then peel the remaining (still attached) stems with a vegetable peeler. Cut one of the lemons in half and rub the artichokes to prevent from turning brown. Place the artichokes in a large pan, add the 2 lemon halves and enough water to almost cover the artichokes. Bring to a boil, cover the pan and cook until the artichokes are tender and the leaves pull away easily, about 30 minutes. Place the artichokes upside down on a towel to drain and cool.
Cut off the stems and mince finely. Carefully pull out the center leaves and scrape out the choke with a spoon leaving the artichoke intact. Discard the center and reserve the minced stems.
In a large skillet, heat the olive oil and butter over medium heat until the butter is melted. Add the anchovies and stir, smashing with the back of a spoon until they have melted into the oil and butter mixture. Add the garlic, red pepper flakes, and minced artichoke stems. Cook for 1 minute, then add the bread crumbs. Cook the mixtures, stirring, until the bread crumbs are nicely toasted. Grate the zest of the remaining lemon into the mixture, squeeze in the juice and add the parsley and parmesan cheese. Taste the mixture and add salt and pepper if needed.
Preheat oven to 400 degrees.
Fill all of the leaves of the artichokes, one by one, with the breadcrumb mixture and add some to the center. Place the artichokes in a Dutch oven or pan with a cover. Add about ¼ inch of water, drizzle the tops of the artichokes with some olive oil, cover the pan and bake for 20 minutes. Remove the cover from the dish and bake for another 10 minutes or until the leaves start to curl up. Can be served hot, warm or at room temperature.