Squeeze the lemons into a large bowl of water, then add the squeezed lemon halves to the bowl. This acidulated water will keep the artichokes from browning.

To clean the artichokes, remove the tough outer leaves until the tender pale-green leaves are exposed. Cut off the top third of each artichoke with a sharp knife. Using a spoon, gently open the center of each artichoke and remove the hairy choke. Trim and peel the stem until it’s smooth and pale. Immediately immerse the cleaned artichoke in the lemon water. Repeat with the remaining artichokes.

In a small bowl, combine the chopped parsley, mint, and garlic. Season the mixture with salt and pepper, then mash or stir until it forms a rough paste. Use your fingers or a small spoon to fill each artichoke cavity with the herb mixture, and rub some over the outer leaves as well. Season the outsides with more salt and pepper.

In a deep, heavy-bottomed saucepan or Dutch oven, pour in the olive oil, wine, and water. Arrange the stuffed artichokes stem-side up in the liquid. Bring to a boil over medium heat.

Once boiling, cover the artichokes with a piece of parchment paper and then cover the pot with a tight-fitting lid. Reduce the heat to low and simmer gently for about 30 minutes, or until the artichokes are tender when pierced with a knife. If needed, continue cooking in 5-minute increments until they are soft throughout.

Transfer the artichokes to a serving dish and spoon over the cooking juices. Drizzle with the remaining olive oil, season with additional salt and pepper, and garnish with fresh parsley and mint leaves. Serve warm or at room temperature.