Boil the eggs until hard (about 9-10 minutes from boiling), cool them in cold water and peel.
Cut the eggs in half and separate the yolks from the whites.
In a bowl, finely chop the onion, then add the capers and the tuna flaked with a fork.
Crumble the egg yolks in as well and mix thoroughly.
In a mortar, crush the garlic with a pinch of salt to a paste, then add the olive oil drop by drop while stirring constantly until you get a thick paste. Stir in the mayonnaise.
Add the garlic mayonnaise to the tuna filling and mix until smooth.
Fill the egg white halves with it and serve on lettuce leaves dressed with olive oil, salt and vinegar.