Boil the potatoes in a big pot of salted water for 8 minutes until almost tender. Add the beans and cook for an additional 2 minutes until crisp-tender. Rinse in cold water, then drain.
Season the tuna generously with salt and pepper. Sear the tuna in hot olive oil for 2 minutes per side for a medium cook or according to your preference. Place the tuna on a plate, tent it with foil, and let it rest for 5 minutes before serving.
Combine anchovy, garlic, and mustard in a mortar and pestle, gently pound until a paste forms. Mix in extra virgin olive oil, vinegar, and basil. Season to taste with salt and pepper.
Cut the tuna into 2cm pieces, then combine it with potato, beans, tomato, olives, radish, and capers in a bowl. Portion into serving bowls, add a boiled egg on top, drizzle with anchovy dressing, and serve with bread.