Place the chicken fillets in a single layer in a shallow dish.
Whisk the oil, parsley and garlic in a bowl.
Add salt and pepper to taste.
Pour the mixture over the chicken.
Turn the fillets several times to coat thoroghly, cover the dish and stand at room temperature for 10 minutes.
Meanwhile, make the dressing.
Combine the anchovy paste or mashed anchvies, garlic, lemon juice, vinegar, oil and egg yolk in a screwtop jar.
Close the lid tightly and shake the dressing until well mixed.
Add salt and pepper to taste.
Arrange the lettuce, cheese and tomatoes in a salad bowl.
Heat a heavy nonstick frying pan over high heat.
Fry the chicken fillets for about 6 minutes or until tender, turning once.
Allow to cool slightly; cut into 1cm (1/2in) wide strips.
Arrange the chicken strips on the salad.
Pour over the dressing, toss gently and serve.