Prepare the artichokes by removing the tough outer leaves until you reach the softer, lighter green leaves inside. Trim the tops and stem, leaving about an inch of the stem attached. Rub all cut surfaces with a lemon half to prevent browning.
Spread the leaves of the artichokes open slightly to expose the center. Remove the fuzzy choke with a spoon, being careful not to break the leaves. Again, rub with lemon to prevent browning.
In a small bowl, combine the minced garlic, lemon juice, parsley, mint, salt, and pepper. Mix to create a herb paste.
Stuff the herb paste into the center and in between the leaves of each artichoke.
Heat the olive oil in a large pan or pot over medium heat. Place the artichokes stem side up in the pan and cook for 5 minutes until the bottoms begin to brown.
Add white wine and water to the pan, then cover and reduce heat to low. Let the artichokes braise for about 35-40 minutes, or until the leaves can be easily pulled off.
Check occasionally and add more water if necessary to prevent burning.
Once cooked, transfer the artichokes to a serving platter and spoon over the cooking liquid.