Rinse lettuce, pat dry and arrange on a platter. Cut the eggs into slices about 5 mm thick and place on the lettuce.
Free red and yellow peppers from seeds and partitions and cut into small cubes. Chop the anchovy fillet. Crush the garlic cloves with a knife. Separate the parsley leaves from the stems and chop.
Heat olive oil in a saucepan over moderate heat. Add pepper, garlic and anchovies. Lower the heat and cook for 7-10 minutes, avoiding the color of the garlic to change. Remove the saucepan from the stove, remove the garlic and add the parsley. Stir.
Pour sauce over eggs, season with sea salt and coarsely ground black pepper.