Make the dressing: mince garlic on a cutting board and sprinkle heavily with salt; using a knife, scrape garlic and salt together to form a smooth paste. Transfer paste to a bowl and whisk in oil, juice, mustard, shallot, and salt and pepper; set aside.
Make the tuna: Pulse all ingredients together in a food processor. Season to taste with lemon and salt, as needed.
Assemble the salad: Toss potatoes with just enough dressing to lightly coat. Arrange lettuce in bowls and in sections add the cucumber, potatoes, beans, tomatoes, olives, and a big scoop of the tuna. Drizzle additional dressing over the salad and top with the chives. Enjoy!