Step 1In a small bowl, whisk together the lemon juice and olive oil. Season to taste with salt and pepper. Cover and refrigerate until needed.
Step 1In a large bowl, whisk the egg yolks together with the lemon. Slowly whisk in the oils, 1 teaspoon at a time, constantly whisking until the oil is emulsified to make a mayonnaise. This makes about 2 cups mayonnaise.
Step 2Using a mortar and pestle, or chopping and crushing with the side of a knife, combine the capers, Worcestershire sauce, garlic and anchovy fillets to form a paste.
Step 3Stir the puree into the mayonnaise until thoroughly combined, then stir in the Parmesan cheese. Season to taste with salt and pepper. This makes about 2 cups dressing, more than is needed for the remainder of the recipe; the remaining dressing will keep for 2 to 3 days, covered and refrigerated.
Step 1In a small saucepan, heat 1 to 2 inches of oil until a thermometer inserted reads 350 degrees. Add the capers and fry for 30 seconds. Drain on a paper towel, then season to taste with salt.
Step 1Heat the oven to 350 degrees. Brush the baguette slices with the oil, then lightly sprinkle over salt and pepper. Place the slices on a baking sheet and toast until crisp and golden, about 4 minutes.
Step 1Quarter each head of lettuce lengthwise, and toss the wedges with the lemon vinaigrette and chopped parsley.
Step 2On each of 4 plates, spoon over a light base of Caesar dressing, then top the dressing on each plate with 4 lettuce quarters.
Step 3Garnish each wedge with a crouton and lemon wedge, and top each crouton with half of an anchovy fillet. Sprinkle over the chopped black olives, fried capers and Parmesan cheese evenly over the 4 servings. Serve immediately.