Remove tough outer leaves of artichokes, halve, remove hairy choke with a teaspoon (discard), slice into thin wedges and toss in lemon juice to prevent discolouring.
Cook eggs in a saucepan of simmering water until soft-boiled (7 minutes), refresh and peel. Halve just before serving.
Meanwhile, blanch beans until bright green (1 minute), refresh, drain and transfer to a large bowl. Add artichoke, tomatoes, radish, parsley, lemon juice and oil, season to taste, toss to combine and set aside.
Preheat grill to high heat. Toast bread, turning once, until golden (1-2 minutes), then rub with garlic. Spread with mayonnaise, top with tuna, then salad and eggs, season to taste and serve.