Pre-heat the oven to 400°F.
Trim the artichokes by cutting off the stems and tops with a knife. Snip the tips of the side leaves with scissors. Rub all the cut surfaces with cut lemon halves. Squeeze the lemons into a large pot, add the juiced lemon halves, and fill the pot halfway with water. Bring to a boil. Add the artichokes to the boiling water and place a small kitchen towel on top; this will keep them submerged. Boil the artichokes until tender, 12-15 minutes, then remove them with tongs and place them upside down on a towel to cool. When they are cool enough to handle, use a teaspoon to scoop out the spiny choke.
While the artichokes cook, heat the 1/2 cup of EVOO in a skillet over medium-low heat. Add the anchovies, garlic, and red pepper flakes and cook for 3-4 minutes, until the anchovies melt away. Add the bread crumbs and toast until deeply golden. Season with parsley and lots of black pepper. Remove from the heat, add the cheese, and toss to combine.
Add 1/4 inch water to a shallow baking dish and arrange the artichokes in the pan. Spoon the filling into each leaf and the center of the artichokes. Drizzle more EVOO over the stuffed artichokes, cover the pan with foil, and bake for 15 minutes to set the stuffing. Remove the foil and bake for another 10 minutes uncovered to crisp up the tops.
Serve out of the hot baking dish with a bowl alongside to catch the leaves.