Bring 3 quarts (2.8L) water to a boil in a large pot and prepare an ice bath. Carefully lower eggs into pot and continue to boil for 30 seconds. Cover tightly, reduce heat to low (water should maintain a bare simmer), and continue cooking for 9 minutes for jammy yolks or 11 minutes for hard-cooked yolks. Immediately transfer eggs to ice water and allow to cool for at least 15 minutes, then peel under cool running water. Quarter eggs lengthwise and set aside.

Meanwhile, if using fava beans, open up fava bean pods and remove individual beans. Discard pods. Bring a medium pot of salted water to a boil and prepare an ice bath. Add fava beans to pot and cook until just tender, about 2 minutes. Transfer fava beans to ice bath and allow to chill for 1 minute. Carefully peel off and discard the outer skin from each bean and set aside.

Core and slice ¾ pound (340g) of tomatoes into ¼-inch-thick wedges; set aside. Split remaining ½ pound (230g) tomatoes in half horizontally. Set a box grater into a large bowl. Rub cut faces of split tomatoes over the large holes of a box grater, using the flattened palm of your hand to move the tomatoes back and forth. The flesh should be grated off, while the skin remains intact in your hand. Discard skin and season tomato pulp with kosher salt to taste.

In a large mixing bowl, combine fava beans (if using), green pepper rings, artichoke heart (if using), breakfast radish (if using), olives, scallions, and basil leaves. Drizzle generously with olive oil and season with salt to taste, and toss to coat evenly (if desired, you can also mix in a light splash of red wine vinegar).

Split rolls in half horizontally and, using your fingers, scoop out and discard some of the tender crumb from both the top and bottom halves. Rub smashed garlic cloves all over cut sides of top and bottom halves of each roll to infuse the bread with garlic flavor. Discard any remaining garlic,. Spoon grated tomatoes all over cut sides of rolls and drizzle with olive oil (you may not need to use all the grated tomatoes).

Lightly season sliced tomatoes with salt, then layer the sliced tomatoes, boiled egg quarters, flaked tuna, anchovy fillets, and dressed vegetables onto the bottom halves of each roll. Drizzle generously with additional olive oil, season with pepper (if desired), then close sandwiches, wrap tightly in parchment, foil, or reusable wrappers and let stand at least 20 minutes or up to 1 hour. Serve.