Bring a pot of water to a boil and add eggs. Cook for about 7-8 min for a slightly jammy egg. Transfer to an ice bath to stop the cooking. When cool enough to touch, peel the eggs.
While the eggs are cooking, start preparing the tuna by mixing tuna with vinegar, olive oil, shallot, capers, olives, lemon, peppers and parsley. Season to taste with salt and pepper. The tuna is should have extra dressing, it’s meant to be an overdressed sandwich.
Slice bread and spoon the tuna mix over top. Add a bit more of the dressing over top. Add fresh basil, sliced hardboiled eggs, tomatoes, sliced red onion and arugula. Drizzle with more red wine vinegar and wrap up sandwich. Sandwich will be better the longer the flavors meld together so it really is the perfect beach sandwich!