Combine the shallots with olive oil, red wine vinegar, parsley, olives, capers, salt, and several grinds of black pepper in a medium to large bowl.
Using a fork, potato masher, or your hands, press/squeeze everything together for a few minutes.
Add the cans of tuna with the oil. Season to taste with fresh lemon juice, more olive oil and red wine vinegar, salt, and pepper.
Cut rolls in half crosswise, drizzle olive oil on each of the halves, add lettuce, tuna, egg, anchovies, and radish to the bottom halves, and cap off with the top halves.