In a heavy saucepan with a lid, combine the wheatberries, water or stock, salt, and bay leaf. Bring to a boil and then simmer partially covered until the wheatberries are pleasantly chewy, which may take anywhere from 50 to 90 minutes. Remove the pan from the heat, discard the bay leaf, and let the berries cool in the liquid. When cool, drain off all the liquid and put the berries into a large mixing bowl. Add the artichoke hearts, tomatoes, roasted pepper, capers, scallion, almonds, and basil or cilantro.
Whisk together the garlic, lime juice, vinegar, olive oil, salt, and pepper; toss with the salad. Arrange the greens on chilled plates and top with the salad.