The key here is to use small artichokes, babies really. You can use large 'chokes, but it is a lot more work and you will need to chop the hearts into three or four pieces. Small artichokes are a commonplace in California farmers' markets, but you might need to order them if you live in a colder clime. But it's worth it. These chokes are firm, fresh-tasting and absolutely delicious -- nothing at all like the preserved artichokes you get in the store.
Put everything but the artichokes in a large pot and bring it to a boil. Cover and turn off the heat.
Fill a canning kettle (I use a stock pot) with enough water to cover the quart Mason jars you will need to can these artichokes. You will need something on the bottom of the pot to keep the glass jars off the bottom. I use a steel veggie steamer with the feet pulled off, or you could use spare jar rims. Put it on medium heat.
Get a large bowl and fill it with cold water. Squeeze 2 lemons into the water and drop the lemons into the bowl. Pick off the tough outer leaves of the artichokes, leaving only the ones that are tightly attached and yellow at the center. Slice off the top of the artichokes, and trim the outer layer off the choke bottom, leaving as much as you can -- you need a sharp knife for this. Rub the artichoke all over with cut lemon and drop it into the bowl with the lemons. This prevents them from oxidizing and turning brown. Repeat until you are done.
Turn the heat back onto the pot with the seasoned vinegar and oil. Put the artichokes in that pot, stir around and bring to a boil. With a slotted spoon, fill the Mason jars 3/4 full with the artichokes. Ladle the vinegar-oil mixture over the chokes evenly. If you run out of sauce, you can add a little vinegar and oil to top off. Make sure the rims of the jars are clean and dry, and that you are using brand-new lids. Close the jars.
Submerge the two jars in the now-boiling water of the stockpot. Let this boil for 15 minutes. Let cool on a cutting board until the artichokes return to room temperature. They will keep a year. Refrigerate after opening.