Fill a large mixing bowl with water. Squeeze the juice of 1 lemon into the water. When you clean the artichokes, put them into this water—the lemon in it will keep the artichoke hearts from turning brown. Quick guide to cleaning artichokes: First, put on rubber gloves, because the artichoke leaves make everything taste bitter, and you don’t want that on your fingers (alternatively, just wash your hands and your cutting board well when you’re done cleaning the artichokes). Rip off the outer leaves of the artichoke until the leaves look light green or yellow. Using a sharp knife, cut off the leaves at their base. Discard the leaves. The choke (the fuzzy prickles in the center of the artichoke) should now be exposed. Use a melon baller to remove and discard the choke. Using a paring knife, separate the stem from the artichoke heart. Save the stem. Remove any dark green from the artichoke heart using the paring knife. The artichoke heart should now be clean, so drop it in the lemon water. Use the paring knife to remove the fibrous outer layer of the stem. The inside of the stem should be a lighter color than the fibrous outside. When the stem is clean, add it to the lemon water. Thinly slice 3 cloves of garlic and set them aside. Set a large skillet over low heat. Add the olive oil, along with the thinly sliced garlic, chile flakes, lemon peel, and 4 sprigs of thyme. Remove the cleaned artichoke hearts and stems from the lemon water, and cut them into bite-size pieces. Add the artichoke to the skillet and adjust the heat to medium. Season with salt and freshly ground black pepper. Cook, stirring occasionally, until the artichokes begin to turn tender (after approximately 10 minutes, taste a piece to see how tender it is). When the artichokes are just tender, add the white wine. Adjust the heat to high and cook for approximately 2 minutes, until the wine has reduced by half. Remove the skillet from the heat, and discard the lemon peel and thyme sprigs. Set a fine mesh strainer over a mixing bowl. Pour the contents of the skillet into the strainer. Transfer the contents of the strainer to a container and store in the refrigerator. Transfer the remaining liquid from the mixing bowl to a large pot. Remove the roots and dark green outer leaves from the leeks. Slice the leeks in half lengthwise and clean them with cold water to remove any dirt. Slice the leeks into thin half-moons. Set the pot with the artichoke oil over medium heat. Add the leeks and cook, stirring occasionally, until they begin to soften. Drain the beans of their soaking water and add the beans to the pot. Add 4 cups of fresh water to the pot and bring the water to a boil. Adjust the heat so that the water is gently simmering. Add the remaining 4 sprigs of thyme, along with the bay leaf. Let the beans cook for at least 2 hours, until they taste soft and creamy. There should be a little liquid left in the pot (it should resemble stew). If too much liquid evaporates during the cooking process, add more water. While the beans are cooking, set a small skillet over medium heat. Add the butter. When the butter is melted and hot, add the breadcrumbs. Stir the breadcrumbs regularly until they become lightly toasted. Rub 1 clove of garlic against a fine microplane, and add the microplaned garlic to the skillet. Stir for 1 additional minute, until the garlic is fully mixed in with the toasted breadcrumbs. Set the garlic breadcrumbs aside. When the beans are soft, creamy, and fully cooked, season them with salt and freshly ground black pepper. Taste the beans. Continue to adjust the seasoning until the beans taste delicious. Add the cooked artichokes, along with the sorrel and the lemon juice. Stir regularly over low heat until the sorrel just begins to wilt, approximately 2 minutes. Serve the cassoulet garnished with a sprinkle of garlic breadcrumbs, and enjoy.