Although the recipe calls for lentils, try making them with yellow split peas as well, for a lovely and sturdy variation. The split peas will need a little more water (up to 2 1/2 cups) and more cooking time, but are a really nice option.
Place the lentils and water in a medium-small saucepan, and bring to a boil. Lower the heat to a simmer, partially cover, and cook for about 30 minutes, or until the lentils are soft and the water is completely absorbed. (Don’t worry about overcooking the lentils. Soft is good in this recipe, and we want all the water gone.) Transfer to a medium-large bowl, add the vinegar, and mash with a fork or a potato masher. Set aside.
Place a medium-sized skillet over medium heat, and wait about a minute. Add 1 tablespoon olive oil, and swirl to coat the pan, then add the onion and sauté for about 5 minutes, or until the onion is translucent. Add all the remaining ingredients except the walnuts and bread crumbs, and sauté over medium heat for 5 to 10 minutes, or until all the vegetables are tender. Turn up the heat for the last minute or so, to let the moisture evaporate.
Stir the sautéed mixture into the lentils, along with the walnuts and breadcrumbs. Mix thoroughly, then cover the bowl (or transfer to a container with a tight-fitting lid) and chill for at least an hour (longer is okay).
Form 4-inch patties about 1 1/2 inches thick, and fry on both sides in a hot, oiled pan until heated through and crispy on the outside. You can also broil them for 5 to 8 minutes on each side (until golden and crisp). Top with some grated cheese at the last minute, if desired, and let it melt.
Serve hot, with desired accoutrements.