Fill a large pot with cold water and squeeze 3 of the lemons into it (this is known as acidulated water). Keep it off the heat for now. The cut artichoke hearts have to head straight into the lemon water to keep them from browning.
Trim the artichokes: Lay an artichoke on its side and trim the brown woody tip of the stem. Using a very sharp or serrated knife, cut the top one-third of the thorny artichoke leaves off, leaving a flattened top. Use your hands to tear off the toughest outermost leaves from around the bottom of the artichoke, leaving most of the leaves untouched. Lay the artichoke on the board again and this time cut it in half lengthwise, from stem to top. Using a paring knife or a peeler, carefully peel off the outermost layer of the stem. Use a spoon to scrape away the inedible furry choke in the center of the artichoke. Voila-you have an artichoke heart! Quick, put it in the acidulated water. Repeat to trim the rest of the artichokes.
Poach the artichokes: Add more water to the pot if needed to cover the artichokes. Season the water with 3 tablespoons salt. Place the pot over medium-low heat and bring the water to a simmer. Poach the artichokes for about 15 minutes, or until they're easily pierced with the tip of a knife. Drain the artichokes. Transfer them to a large bowl and set aside.
Marinate the artichokes: In a large saucepan, heat 2 tablespoons olive oil over medium-low heat. Add the garlic halves cut-side down and sear them until lightly golden, 3 to 4 minutes. Add the thyme and tarragon. Squeeze the remaining 3 lemons into the pan and throw in the squeezed lemon halves as well. Add the wine and simmer on high heat until it has reduced by half, about 5 minutes. Add the remaining 4 cups olive oil and the remaining 1/2 teaspoon salt. Bring the marinade to a boil, then turn off the heat.
Carefully pour the hot marinade over the artichokes and stir to combine. Transfer the artichokes and marinade to mason jars with lids or airtight containers and refrigerate. Marinate for at least 1 hour, but ideally overnight, before serving. Store them in the refrigerator for up to 10 days.
Photograph by David Malosh
Courtesy of Food Network Magazine