1. In a small glass or stainless-steel bowl, whisk together the lemon juice, thyme, 1/2 teaspoon each of the salt and pepper. Whisk in the 1/3 cup of oil.
2. Remove the soft centers of the rolls, leaving a 1/2-inch shell. Rub the garlic on the inside of each and brush with the 2 tablespoons oil.
3. Top the bottoms of the rolls with the lettuce. Layer with half the tomato slices and the chicken; sprinkle with 1/8 teaspoon each of salt and pepper. Top with half the slices of egg, onion, and bell pepper, and half the olives, and then drizzle with half the dressing. Repeat with the remaining tomato, chicken, 1/8 teaspoon each salt and pepper, egg, onion, bell pepper, olives, and dressing. Top with the anchovies, if using. Cover with the tops of the rolls. If you have time, wrap each roll tightly in aluminum foil; let sit for 10 minutes. Otherwise, press down on the rolls firmly so that the dressing moistens the bread.
Menu Suggestions: You really don't need anything with this, but roasted potato wedges would be nice.
Wine Recommendation: The south-of-France flavor of this sandwich is perfect with the delicate, herbal notes found in many rosés from Provence. Bottles from the Coteaux du Varois, Cassis, or Bandol would all be good possibilities.