For the White Bean Puree: Soak the beans overnight. Or place beans in a pot, cover with cold water and bring to a boil over high heat; remove from heat and set aside, covered, for 1 hour. Drain the beans; transfer to a 2-quart pot with the diced onion, smashed garlic, bay leaf, thyme sprigs, 5 cups of stock, and salt and pepper, to taste. Bring to a boil. Lower the heat; simmer until beans are very tender and are breaking apart, about 2 hours. If the mixture becomes dry, add some of the remaining stock. Drain the beans; discard the thyme sprigs and bay leaf. Puree the beans in a food processor, adding a few drops of oil. Adjust seasonings with salt and pepper, to taste, along with the lemon juice, white vinegar, and walnut oil, if desired. Reserve.
For the Olive Tapenade: In a food processor or mortar, combine the olives, capers, lemon zest, garlic, parsley, and salt and pepper, to taste. Slowly add the oil and pulse or work with the pestle into a coarse paste, retaining some bits of olive and caper for texture. Taste to adjust the seasonings. Reserve.
Sandwich Assembly: Smear with white bean puree on 4 pieces of potato bread. Arrange sliced tuna on top. Drizzle tapenade over tuna. Add sliced tomatoes, sliced egg and dressed French green beans. Top with greens and toasted bread. Garnish with basil and arugula.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.