Halve the lemon and squeeze the juice into a large bowl of cold water. Add the lemon halves to the bowl.
Peel off the tough outer leaves of the artichokes (one at the time) and trim 1 inch from the top (as shown in the pictures).
In a medium bowl, combine garlic, parsley, mint, salt, and 1 tablespoon of the olive oil.
Place 1 tablespoon of the herb mixture in the cavity of each artichoke and arrange in a deep frying pan or heavy pot that holds them close together. A Dutch oven works well for this.
Add the wine, water, remaining oil, and a dash of salt.
Bring to a light boil, then turn to low heat, cover, and simmer for 50 to 60 minutes or until tender.