Fill a large bowl with water and squeeze in two lemons, then add the halved lemons into the bowl.
Clean the artichokes, removing the hardest outer leaves, until you reach the heart of the artichoke, which has lighter and tender leaves. Cut the prickly tip of the artichoke and trim the base. Rub the artichoke with half of a lemon and plunge the cleaned artichoke heart into the bowl of water. Do the same for all the baby artichokes.
Pour the water and the vinegar into a large pot, then bring them to a boil over medium heat. When they start to boil, add the salt and then all the artichokes.
Cook over medium heat for 5 to 7 minutes, or until the artichokes are so soft that they can be easily pierced with the tip of a knife.
Drain the artichokes and arrange them standing, cut side down, in a tray covered with a clean tea towel. Cover them with another tea towel and leave them dry for at least a day, until they have drained all the excess water.
When the artichokes are ready, pour a few tablespoons of olive oil on the bottom of the jars, then fill them with the artichokes, placing them one next to the other. Sprinkle a few peppercorns between one layer and the another.
Fill the jars with olive oil covering the artichokes. Check again after a few hours to see if you need to pour in more olive oil to completely cover the artichokes. Close the jars and store them for a few months in the pantry, or in a dry, cool and dark place.