Cut each of the artichokes in half, remove the tough outer leaves and any choke that you find (ours shouldn’t have much), and trim the bottom 1/2-inch off of the stem.  Put 3 tablespoons of butter in a large, deep skillet over medium high heat.  When the foam subsides, add the artichokes, cut side down.  Cook until lightly browned, about 5 minutes.  Add the stock, bring to a boil, and cover.  Turn down the heat to medium low.  Cook for about 20 minutes, or until tender.  If you start to run out of stock, add a bit more stock or water.  When the artichokes are tender, sprinkle with salt and pepper to taste, and transfer to a serving platter.  Raise the heat to medium high and cook, stirring occasionally, until the liquid is reduced to a sauce.  Stir in the lemon zest and juice and remaining tablespoon of butter.  Taste and adjust the salt and pepper as needed.  Drizzle the artichokes with the sauce.