Dice the potatoes into 1cm cubes. In a bowl combine the potatoes, garlic and 2 tablespoons olive oil and toss until the potatoes are well coated. Place in a baking pan and roast 45 minutes or until golden and crunchy. Drain on paper towels and sprinkle with salt. Let cool about 10 minutes.
In a bowl, mash the anchovy fillets into the remaining 4 tablespoons olive oil. Add Worcestershire and lemon juice.
Tear up the cos lettuce into chunks and toss with the dressing. Sprinkle over some salt and pepper and toss again. Break in the eggs and toss once more. Add the warm potatoes and sprinkle with cheese and serve at once so it doesn't wilt.